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OF    ILLINOIS 


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AGRICW.TURE 


NON  CIRCULATING 

CHECK  FOR  UNBOUND 
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UNIVERSITY  OF  ILLINOIS 

Agricultural  Experiment  Station 


BULLETIN  No.'  302 


GROWTH  AND  SENESCENCE  IN 
PUREBRED  JERSEY  COWS 


BY  F.  A.  DAVIDSON 


URBANA,  ILLINOIS,  JANUARY,  1928 


CONTENTS 

PAGE 

INTRODUCTION : 183 

THE  PROBLEM 184 

SOURCE  OF  DATA 185 

BIOMETRICAL  ANALYSIS  OF  DATA 185 

Course  of  Growth  in  Register-of -Merit  Jersey  Cows  as  Described  by  In- 
crease in  Body  Weight  with  Advancing  Age 185 

Truncation  of  Yearly  Butterfat  Frequency  Distributions  Due  to  Selective 

Effect  of  Register-of-Merit  Requirement 199 

Comparison  of  Means  (V)  and  Standard  Deviations  (a)  on  Original  Scale 

with  Means  (a)  and  Standard  Deviations  (s)  on  Logarithmic  Scale .   209 
Course  of  Growth  and  Senescence  as  Described  by  Rise  and  Fall  in  Yearly 

Butterfat  Yields  with  Advancing  Age 212 

Influence  of  Level  of  Production  Upon  Age  Curve  of  Milk  Secretion 223 

Nature  of  Selection  of  Register-of-Merit  Production  Requirement 224 

SUMMARY 225 

Course  of  Growth  in  Body  Weight 226 

Course  of  Growth  and  Senescence  as  Described  by  Rise  and  Fall  in  Yearly 

Butterfat  Yields  with  Advancing  Age 226 

LITERATURE  CITED 229 

APPENDIX..  .  231 


GROWTH  AND  SENESCENCE  IN 
PUREBRED  JERSEY  COWS 

BY  F.  A.  DAVIDSON* 

INTRODUCTION 

The  American  Jersey  Cattle  Club  early  established  a  special  regis- 
ter known  as  the  Register  of  Merit,  in  which  all  purebred  Jersey  cows 
are  eligible  to  entry  upon  the  fulfilment  of  a  minimum  milk-produc- 
tion requirement.  This  requirement  is  based  upon  the  pounds  of  but- 
terfat  produced  during  a  single  lactation  and  varies  linearly  with  the 
age  of  the  cows.  Any  purebred  Jersey  cow  may  have  her  production 
record  entered  in  the  Register  of  Merit  as  many  times  as  she  meets  the 
requirement  for  the  age  at  which  her  production  is  made.  The  cows 
that  have  only  one  record  entered  in  the  Register  are  spoken  of  as 
original-entry  cows,  those  having  more  than  one  record  entered  are 
spoken  of  as  reentry  cows.  Many  thousands  of  entries  have  been 
made  in  the  Register  with  the  result  that  a  large  body  of  data  on  the 
milk  production  of  Jersey  cows  has  accumulated.  These  production 
records,  however,  are  not  quite  representative  of  the  production  records 
of  the  purebred  cows  composing  the  breed  as  a  whole  owing  to  the 
selective  and  environmental  influences  imposed  upon  the  cows  entered 
in  the  Register. 

Gowen  (1920)  pointed  out  that  the  production  requirement  made 
by  the  Register  of  Merit  eliminates  many  of  the  low-producing  cows 
of  the  breed,  which  results  in  the  truncation  of  the  yearly  butterfat- 
yield  frequency  distributions  of  the  Register  eows  at  successive  ages. 
Gowen,  altho  recognizing  this  selective  effect  of  the  production  require- 
ment, made  no  effort  to  correct  for  it  and  instead  used  the  production 
records  of  a  single  herd  of  purebred  Jersey  cows  as  representative  of 
the  productions  of  the  cows  in  the  breed  as  a  whole. 

It  is  a  common  practice  among  breeders  to  provide  the  best  possi- 
ble environment,  from  the  standpoint  of  both  growth  and  production, 
for  the  cows  they  intend  to  submit  for  entry  in  the  Register  of  Merit. 
Hence  the  reentry  cows  have  a  better  chance  to  develop  than  the  origi- 
nal-entry cows,  since  they  are  subjected  for  more  than  one  lactation  to 


•This  investigation  was  started  by  Mr.  Davidson  when  a  member  of  the  Dairy  Department 
of  the  University  of  Illinois  and  was  completed  by  him  under  the  •  direction  of  Professor  Sewall 
Wright  at  the  University  of  Chicago.  The  author  wishes  to  express  his  appreciation  to  Professor 
Wright  for  his  guidance  and  many  valuable  suggestions  during  the  progress  of  the  study. 

Submitted   for  publication  September   14,   1927. 

183 


184  BULLETIN  No.  302  [January, 

an  environment  highly  stimulating  to  growth.  Kildee  and  McCandlish 
(1916),  Eckles  (1918,  1920),  and  McCandlish  (1920)  all  have  demon- 
strated very  clearly  the  influence  of  environment  upon  the  rate  of 
growth  and  milk  secretion  in  dairy  cows.  Cows  provided  with  the  best 
possible  environment  show  a  distinctly  superior  rate  of  growth  and 
milk  production.  There  is  also  an  inclination  among  breeders  to  select 
only  the  highest-producing  cows  in  their  herds  to  submit  for  reentry 
in  the  Register  of  Merit.  Such  a  practice  would  have  a  tendency  to 
bring  about  a  genetic  superiority  of  the  reentry  cows  over  the  original- 
entry  cows  from  the  standpoint  of  milk  production.  This  difference 
between  the  reentry  and  original-entry  cows,  altho  never  actually 
demonstrated  by  the  breeders,  has  long  been  recognized  by  them,  and 
as  will  be  shown  later,  is  not  without  justification. 

Since  the  reentry  cows  are  kept  under  an  environment  which  gives 
them  a  better  chance  to  develop  than  the  original-entry  cows  and  since 
the  former  are  also  subject  to  selection  by  the  breeders,  it  does  not 
seem  logical  to  lump  the  records  of  both  the  reentry  and  original-entry 
cows  together  when  using  them  to  make  a  study  of  the  course  of 
growth  and  senescence  in  purebred  Jersey  cows.  Many  investigators — 
Pearl, Gowen,  and  Miner  (1919),  Hooper  (1921),  Brody,  Ragsdale,  and 
Turner  (1923a),  Turner,  Ragsdale,  and  Brody  (1924),  and  Graves  and 
Fohrman  (1925) — have  used  these  Register-of -Merit  records  for  this 
purpose,  but  with  the  exception  of  Graves  and  Fohrman,  all  have 
lumped  the  original-entry  and  reentry  records  together  in  their  studies. 
The  latter  have  been  the  only  investigators  to  separate  the  original- 
entry  from  the  reentry  records  and  study  them  separately.  The  results 
from  this  investigation,  which  will  be  discussed  in  more  detail  in 
another  section,  show  that  there  is  a  marked  difference  between  the 
original-entry  and  reentry  cows,  as  measured  by  the  rise  and  fall  in 
their  yearly  butterfat  productions  with  advancing  age. 

THE  PROBLEM 

In  this  study  the  Register-of-Merit  records  of  the  original-entry 
and  reentry  Jersey  cows  have  been  analyzed  separately  by  means  of 
biometrical  methods  from  the  following  points  of  view: 

1.  The  course  of  growth  in  Register-of-Merit  Jersey  cows  as  de- 
scribed by  the  increase  in  their  body  weights  with  advancing  age. 

2.  The  course  of  growth  and  senescence  in  Register-of-Merit  Jer- 
sey cows  as  described  by  the  rise  and  fall  in  their  yearly  butterfat 
yields  with  advancing  age.     This  involved  the  preliminary  problem 
of  correcting  for  the  truncation  of  the  yearly  butterfat  frequency  dis- 


1928]  GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows  185 

tributions  at  successive  ages,  due  to  the  selective  effect  of  the  Regis- 
ter-of-Merit  production  requirement. 

3.  A  comparison  of  the  course -of  growth  and  senescence  in  the 
original-entry  and  reentry  cows. 

SOURCE  OF  DATA  % 

The  Register-of-Merit  records  involved  in  this  study  consist  of 
all  of  the  365-day  original-entry  and  reentry  records  as  published  in 
the  yearly  volumes  of  the  Register  of  Merit  up  to  and  inclusive  of  the 
volume  for  1920.  These  volumes  contain  9,694  original-entry  records 
and  2,628  reentry  records,  or  a  total  of  12,322  records  in  all.  Each 
record  as  published  in  the  Register  of  Merit  includes  the  following 
items  of  information  concerning  the  cow. 

1.  Age  at  the  beginning  of  the  lactation  period 

2.  Weight  at  the  beginning  of  the  lactation  period 

3.  Length  of  the  record  in  days 

4.  Total  milk  yield 

5.  Total  butterfat  yield 

6.  Percentage  of  butterfat  in  the  milk 

7.  Designation  of  entry,  whether  first,  second,  etc. 

BIOMETRICAL  ANALYSIS  OF  DATA 

COURSE  OF  GROWTH  IN  REGISTER-OF-MERIT  JERSEY  Cows  AS  DESCRIBED 
BY  INCREASE  IN  BODY  WEIGHT  WITH  ADVANCING  AGE 

Dairy  cows  are  peculiar  in  that  they  show  very  little,  if  any, 
tendency  to  fattening,  this  being  especially  true  of  Register-of-Merit 
Jersey  cows.  Hence  the  increase  in  the  body  weights  of  these  cows  with 
advancing  age  may  be  used  as  a  fair  measure  of  their  rate  of  growth. 

The  frequency  distributions  of  the  body  weights  for  the  Register- 
of-Merit  Jersey  cows  at  successive  ages  following  1.5  years  of  age  for 
the  original-entry  cows  and  2.5  years  of  age  for  the  reentry  cows,  are 
reported  in  Tables  1  and  2  and  Figs.  1  and  2  respectively.  The  histo- 
grams in  Figs.  1  and  2  all  tend  towards  the  symmetrical  or  normal  type. 
These  histograms,  however,  are  not  representative  of  the  true  type  of 
frequency  distribution  of  body  weight,  owing  to  the  fact  that  the  body 
weights  of  the  cows  are  in  part  estimated.  The  original-entry  records 
include  1,096  records  for  which  actual  body  weights  of  the  cows  are 
listed.  These  records  were  analyzed  separately  and  the  frequency 
distributions  of  body  weight  for  these  cows  are  reported  in  Table  3 
and  the  last  four  distributions  in  Fig.  1.  The  fitted  histograms  in  Fig.  1 
may  be  assumed  to  represent  the  true  type  of  distribution  of  body 
weight  for  Jersey  cows.  It  will  be  noticed  that  these  frequency  dis- 


186 


BULLETIN  No.  302 


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1928} 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


189 


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esansaassnausus 

?1 

c 

8 

I 

o 

°.                                                                                           CO 

*The  age 
**The  es 

-.CNCNCOCOf  f  lOUSCOCCK.t-COCOOSO.-CN 

1928] 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


191 


factors  affecting  the  body  weights  of  these  cows  tend  to  have  constant 
percentage  effects,  rather  than  constant  absolute  effects,  thruout  the 
entire  scale.  McAlister  (1879)  has  shown  that  this  type  of  frequency 
distribution  can  be  fitted  by  the  log-transformed  equation  of 
the  normal  frequency  curve,  the  equation  of  the  curve  being  y  = 


=  e  in  which  W  —  body  weight,  y  =  the  ordinate, 

and  a  and  s  are  the  mean  and  standard  deviation  on  the  log  scale.  In 
order  to  make  certain  that  the  frequency  distributions  of  the  actual 
body-weight  data  were  of  the  above-mentioned  skewed  type,  they  were 
fitted  by  both  the  normal  frequency  curve  and  the  log-transformed 
frequency  curve,  the  constants  of  which  are  reported  in  Table  4.  In 
this  table  are  also  included  the  x2  and  probability  values  (P)  measur- 


*   •  fill  orq/rratertfry  ccwe 
-«-«  Ory/'naffitfrf  Ctwa   *i/k  actual 


Age  /M  Years  (Jttwer  clat)  lifiifo) 

FIG.  3. — MEAN  BODY  WEIGHTS  OF  ORIGINAL-ENTRY  Cows 


ing  the  goodness  of  fit  of  these  curves.  In  every  case  it  will  be  found 
that  the  log-transformed  frequency  curve  gives  the  better  fit  to  the 
data.  The  fitted  curves  in  Fig.  1  are  the  log-transformed  curves. 

Altho  the  frequency  distributions  of  the  estimated  plus  the  actual 
body-weight  data  do  not  represent  the  true  type  of  frequency  distri- 
bution of  body  weight,  the  means  of  these  distributions  show  practi- 
cally the  same  trend  with  advancing  age  as  do  the  means  of  the  actual 
body-weight  distributions  (see  Table  5  and  Fig.  3).  Gowen  (1925) 
made  a  comparison  between  the  estimated  and  actual  weights  of  pure- 
bred Holstein  cows  and  found  that  the  means  and  standard  deviations 
were  practically  the  same  in  the  two  sets  of  data.  Hence  owing  to  the 


192 


BULLETIN  No.  302 


[January, 


03 

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192S] 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


193 


advantages  provided  by  the  larger  numbers,  the  estimated  and  the 
actual  weights  were  combined  in  studying  the  course  of  growth  as  de- 
scribed by  the  increase  in  body  weight  with  advancing  age  in  both  the 
original-entry  and  reentry  cows. 

The  statistics  of  the  frequency  distributions  of  body  weight  for 
both  the  original-entry  and  reentry  cows  are  reported  in  Table  6. 
Altho  the  mean  body  weights  of  the  reentry  cows  are  much  greater 
than  the  mean  body  weights  of  the  original-entry  cows,  the  coefficients 
of  variation  are  very  much  the  same  in  both  sets  of  data.  Hence  the 
most  significant  difference  between  these  two  groups  of  cows  lies  in 
the  greater  size  of  the  reentry  cows. 


"ye   m    Yean  (Jtvitr  clot*  l 

FIG.  4. — Lodo  OP  OBSERVED  AND  CALCULATED  MEAN  BODY 
WEIGHTS  OF  REENTRY  AND  ORIGINAL- 
ENTRY  Cows 

The  mean  body  weights  of  the  original-entry  and  reentry  cows 
reported  in  Fig.  4  increase  with  advancing  age  up  to  the  age  of  approx- 
imately 8  years,  where  they  reach  their  maximum  and  after  which 
they  remain  more  or  less  constant.  The  course  of  development  of 
these  Register-of-Merit  cows  as  described  by  the  increase  in  their  body 
weight  with  advancing  age  may  be  expressed  in  the  form  of  a  math- 
ematical equation  representing  their  rate  of  growth.  Accordingly  the 
next  step  in  the  analysis  consists  in  the  selection  of  a  growth  curve 
which  best  represents  the  data  and  which  also  has  a  logical  interpre- 
tation from  the  biological  point  of  view. 

Growth  Curves  Applied  to  Individual  Growth  in  Animals 

Review  of  Literature. — It  was  early  recognized  that  growth  in  animals  is 
cyclic  in  nature  and  does  not  consist  of  a  single  uninterrupted  progression  from 
birth  to  maturity.  Each  growth  cycle  consists  first  of  a  period  of  slow  growth, 


194  BULLETIN  No.  302  [January, 

followed  by  a  period  of  relatively  rapid  growth,  which  in  turn  is  succeeded 
by  a  period  of  slow  growth.  The  curve  representing  a  growth  cycle  is  of  the 
rising  and  falling  type  and  tends  to  be  symmetrical  around  its  center,  the 
maximum  of  the  cycle.  This  cyclic  nature  of  growth  has  been  described  by 
Minot  (1891)  and  Read  (1912)  in  guinea  pigs,  Donaldson  (1915)  in  the  rat, 
Ostwald  (1908)  and  Robertson  (1916)  in  mice,  Robertson  (1923)  in  man,  and 
Brody  and  Ragsdale  (1922)  in  cattle,  sheep,  and  other  domestic  animals. 
According  to  the  theories  of  growth  developed  by  Loeb  (1906),  Ostwald 
(1908),  and  Robertson  (1923),  growth  under  normal  conditions  is  limited 
by  a  series  of  consecutive  autocatalytic  monomolecular  chemical  reactions  and 
the  middle,  or  maximum,  of  each  growth  cycle  represents  the  middle  of  the  re- 
spective limiting  chemical  reaction.  The  equation  of  the  autocatalytic  monomole- 

dx 

cular  chemical  reaction  as  derived  by  Robertson  (1923)  is    --  =  ki  x   (A  —  z). 

at 

A  in  this  equation  represents  the  ultimate  amount  of  growth  attainable  in 
the  cycle  in  question  and  theoretically  determines  the  quantity  of  the  growth- 
promoting  substance  present  at  the  beginning  of  the  cycle  and  exhausted  during 
its  course,  x  is  proportional  to  the  amount  of  this  substance  converted  at  any 
time  t,  and  fci  is  a  constant  determining  the  velocity  of  growth.  On  plotting 

dx 

-fa   for  various  values  of  x,  a  symmetrical  curve  of  the  rising  and  falling  type  is 

obtained  with  a  maximum  where  x  =  y>A.  When  integrated  this  equation  assumes 

/»• 

the  form  of  log    — —    -  =  KA(t  —  ti)  which  when  plotted  gives  an  S  curve  with 
A  —  X 

a  point  of  inflection  at  its  center.  The  formula  embodied  in  this  equation  has 
been  applied  with  more  or  less  success  by  Robertson  (1923)  and  Brody  (1922)  to 
the  growth  cycles  in  man,  mice,  rats,  guinea  pigs,  rabbits,  cattle,  sheep,  swine,  and 
chickens. 

Brody  and  Ragsdale  (1921)  have  shown  that  growth  in  the  dairy  cow  con- 
sists of  two  extrauterine  cycles  and  one  intra uterine  cycle.  Data  on  purebred 
Holstein  cows  and  purebred  Jersey  cows  were  presented  to  show  the  extrauterine 
cycles.  The  first  extrauterine  cycle  commences  slightly  before  birth,  reaches  its 
maximum  at  about  5  months  of  age  and  continues  to  the  age  of  15  months.  The 
second  cycle  begins  immediately  after  the  first,  reaches  its  maximum  at  about  20 
months  of  age  and  continues  to  the  age  of  maturity.  Hence  growth  in  dairy 
cows,  after  the  age  of  2  years,  is  non-cyclic  in  nature  and  follows  an  uninter- 
rupted progression  to  maturity.  Brody  next  turned  his  attention  to  the  growth 
of  Register-of -Merit  Jersey  cows  (Brody,  Ragsdale,  and  Turner,  1923a),  com- 
bining the  weights  of  the  original-entry  and  reentry  cows.  These  data,  as  has 
been  shown,  represent  the  course  of  growth  after  the  age  of  2  years  and  are  non- 
cyclic  in  nature.  A  quotation  from  Brody  will  best  express  his  views  in  regard  to 
these  data.  "The  data  show  that  after  the  age  of  2  years  the  rate  of  growth  de- 
clines in  a  non-cyclic  manner.  The  course  of  decline  in  growth  follows  the  course 
of  decline  of  a  monomolecular  chemical  reaction;  that  is,  the  percentage  decline 
in  growth  with  age  is  constant."  The  equation  of  the  monomolecular  chemical 
reaction  used  by  Brody  et  al  is  W=  A  (1 — e-*0  where  A  represents  the  weight 
of  the  animal  at  maturity,  W  the  weight  of  the  animal  at  any  time  t,  and  k  the 
velocity  constant  of  growth.  This  equation  when  applied  to  the  data  gives  a 
fairly  good  fit.  Later  Brody  and  Ragsdale  (1924)  attempted  to  reach  a  growth 


1928}  GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows  195 

equation  representing  the  whole  course  of  development  from  birth  to  maturity. 
The  Department  of  Animal  Husbandry  of  the  University  of  Missouri  has  for 
years  been  collecting  a  large  number  of  linear  measurements  and  body  weights 
of  purebred  Jersey  cows  at  intervals  from  birth  to  maturity.  These  data  were 
used  by  Brody  to  represent  the  whole  course  of  development  in  Jersey  cows  from 
birth  to  maturity.  The  cyclic  fluctuations  are  obvious  in  these  data,  but  in  the 
present  study  they  were  not  considered.  The  growth  equation  derived  by  Brody 
to  fit  the  data  is  W  =  A — Be~kt  where  W  is  the  weight  or  linear  dimension  at  any 
time  t ,  A  is  the  limit  reached  at  maturity,  k  is  the  velocity  constant  of  growth,  and 
Bis  a  constant  locating  the  curve  in  point  of  time.  This  equation  has  the  same  form 
as  the  equation  of  a  monomolecular  chemical  reaction  with  the  exception  that  in 
a  monomolecular  reaction  A  and  B  have  the  same  value  and  the  curve  begins  at 
zero.  Brody's  interpretation  of  the  curve  is  as  follows:  "Barring  fluctuations  due 
to  the  cyclic  phenomena,  the  extrauterine  course  of  growth  in  linear  dimensions 
and  in  weight  of  the  dairy  cow  follows  an  exponential  law  having  the  same  form 
as  the  law  representing  the  course  of  monomolecular  change  in  chemistry.  This 
suggests  the  interpretation  that  the  general  course  of  growth  is  limited  by  a 
monomolecular  chemical  process,  and  that  the  cyclic  phenomena  are  due  to  sub- 
sidiary processes  in  the  fundamentally  exponential  course  of  growth.  .  .  .  This  is 
in  accordance  with  expectations  if  it  is  assumed  that  each  animal  begins  life  with 
a  definite  endowment  of  limiting  substance  necessary  for  the  process  of  growth, 
and  that  this  endowment  is  used  up  at  a  constant  rate  (or  percentage)  of  itself." 
In  a  later  paper  Brody  (1926)  gives  a  somewhat  different  interpretation.  "One 
may,  of  course,  with  equally  good  logic,  interpret  this  equation  as  indicating  the 
production  during  the  course  of  growth  of  a  growth-retarding  substance  according 
to  the  monomolecular  law." 

Altho  there  seems  to  be  a  striking  similarity  between  the  course  of  growth 
in  animals  and  the  course  followed  by  a  monomolecular  chemical  reaction,  it 
seems  doubtful  whether  such  a  complicated  process  as  growth  would  follow  so 
simple  a  chemical  reaction.  The  same  criticism  holds  true  for  the  autocatalytic 
monomolecular  theory  of  growth.  The  S  curve  of  the  autocatalytic  monomole- 
cular reaction  is  a  rather  flexible  curve  and  can  be  made  to  approximate  closely  a 
great  many  growth  reactions  in  both  animals  and  plants.  However,  the  point  of 
inflection  of  this  curve  is  at  its  center,  whereas  most  of  the  growth  reactions  show 
a  point  of  inflection  earlier  in  the  reaction.  Van  de  Sande-Bakhuyzen  and  Als- 
berg  (1927)  have  given  a  very  thoro  criticism  of  the  autocatalytic  monomolecular 
chemical  theory  as  applied  to  growth  in  animals  and  plants  and  have  presented 
evidence  to  show  that  the  reactions  involved  in  growth  cannot  be  represented  by 
such  a  simple  chemical  theory. 

A  growth  curve  similar  to  that  derived  by  Brody  (1924)  but  with 
a  more  general  biological  meaning  may  be  derived  in  the  following 
manner.  Minot  (1908)  showed  for  a  number  of  animals  that  the  per- 

\y  —  w 
centage  increments  in  body  weight. — *-=-, —  — ,  constantly  decrease  from 

"x 

birth  to  maturity.  These  percentage  increments  may  be  looked  upon 
as  measuring  the  average  growth  power  of  the  body  cells,  if  growth 
power  may  be  defined  as  the  percentage  rate  of  increase  in  growth. 


196  BULLETIN  No.  302  [January, 

Wright  (1926)  suggested  briefly  that  the  hypothesis  that  growth 
power  falls  off  at  a  constant  percentage  rate  leading  to  the  curve 

/» 

log  log  —    =  a  —  kt  might  often  give  a  good  fit  to  growth  data.  This 

curve  may  also  be  expressed  in  the  form  log  W  =  A  —  be  ~  kt,  curiously 

similar  to  Brody's  formula.  The  derivation  of  this  equation  is  as 
follows: 

dW 

Wdt=P  (1) 

where  W  =  body  weight  at  any  time  t,  and  P  =  growth  power  of  the 
body  cells.  Since  the  growth  power  is  assumed  to  fall  off  at  a  constant 
percentage  rate, 

—  -        k 

Pdt  ~ 

log  P  =  C  -  kt 


P-  eC~kt  --  (3) 

Wdt 

logF  =  -  \eC~kt  + 

K 

ec     -  kt 


In  equation  (4)  A  is  the  logarithm  of  the  weight  of  the  animal  at 
maturity;  lOOfc  is  the  constant  percentage  rate  of  decrease  in  growth 
power  on  the  above  interpretation,  and  b  locates  the  curve  in  time; 
W  is  the  weight  at  any  time  t.  This  equation  differs  from  Brody's 
growth  equation  in  that  W  is  replaced  by  log  W  and  A  is  the  logarithm 
of  weight  instead  of  the  actual  weight  at  maturity.  Also,  it  does  not 
involve  any  simple  chemical  interpretation  of  growth.  The  curve  for 

weight  (W)  is  «S-shaped  with  the  point  of  inflection  at  -  =  37  percent 

e 

of  the  final  weight. 

We  may  now  turn  to  the  growth  data  of  the  original-entry  and  re- 
entry Register-of-Merit  Jersey  cows  presented  in  Table  6.  Equation 
(4)  was  applied  to  these  data,  and  the  values  calculated  from  the  fitted 


1928} 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


197 


equations  are  reported  in  Table  7.  The  fitted  equations  for  original- 
entry  and  reentry  cows  are  respectively : 

loglo  W  =  2.9793  -  .1273446-'2763' 
loglo  W  =  2.9930  -  .134378e~  •2993' 

In  these  equations  t  =  age  and  is  measured  in  units  of  six  months  be- 
ginning with  one  year  and  three  months  as  the  origin.  W  =  weight 
at  any  age  t. 

TABLE  7. — MEAN  BODY  WEIGHTS  FOR  ORIGINAL-ENTRY  AND  REENTRY  JERSEY 
Cows  WITH  ADVANCING  AGE 


Age  in  years 

Original-entry 

Reentry 

Mean 
observed 

Logio 
Mean 
observed 

Logio 
Mean 
calculated 

Mean 
ob- 
served 

Logio 
Mean 
observed 

Logio 
Mean 
calculated 

1.5-2.0 

766 

2  .  88423 

2  .  88270 

2.0- 

808 

2.90741 

2.90602 

2.5- 

836 

2.92211 

2.92371 

870 

2!  93952 

2.93826 

3.0- 

867 

2.93802 

2.93713 

911 

2.95952 

2.95242 

3.5- 

881 

2.94498 

2.94731 

907 

2.95761 

2.96292 

4.0- 

906 

2.95713 

2.95503 

940 

2.97313 

2.97070 

4.5- 

922 

2.96473 

2.96089 

942 

2.97405 

2.97647 

5.0- 

925 

2.96614 

2.96534 

949 

2.97727 

2.98074 

5.5- 

931 

2.96895 

2.96871 

964 

2.98408 

2.98391 

6.0- 

937 

2.97174 

2.97126 

973 

2.98811 

2.98626 

6.5- 

933 

2.96988 

2.97320 

973 

2.98811 

2.98801 

7.0- 

934 

2.97035 

2.97468 

982 

2.99211 

2.98930 

7.5- 

940 

2.97313 

2.97579 

983 

2.99255 

2.99026 

8.0- 

944 

2.97497 

2.97664 

982 

2.99211 

2.99097 

8.5- 

944 

2.97497 

2.97728 

996 

2.99826 

2.99149 

9.  fl- 

961 

2.98272 

2.97795 

966 

2.98498 

2.99202 

lC.  0- 

964 

2.98408 

2.97852 

949 

2.97727 

2.99246 

11.0- 

943 

2.97451 

2  .  97885 

1007 

3.00303 

2.99271 

12.0-13.0 

960 

2.98227 

2.97904 

954 

2.97955 

2.99283 

14.1* 

950 

2.97772 

2  .  97920 

14.5* 

l6i2 

3!  00518 

2.99299 

The  equations  of  the  curves  fitted  to  observed  values  are:  original-entry,  logio  W  •• 
.127344e--z™»<;  reentry,  logio  W  =  2.9930  - .  134378e-»«»«<. 

*Average  age  of  cows  ranging  from  13.0  to  18.5  years  of  age. 


2.9793  - 


The  smooth  curves  in  Fig.  4  describing  the  course  of  growth  in 
body  weight  of  the  original-entry  and  reentry  Jersey  cows  are  the 
fitted-growth  curves  represented  by  the  above  equations.  It  will  be 
noted  that  the  trends  of  these  curves  closely  agree  with  the  trends  of 
the  observed  mean  body  weights  with  advancing  age.  Therefore  it 
may  be  assumed  that  growth  power  in  body  weight  of  the  original- 
entry  and  reentry  Jersey  cows  after  2  years  of  age  is  falling  off  at  a 
fairly  constant  percentage  rate.  It  should  be  noted  that  this  curve 
cannot  be  carried  back  to  birth  on  this  basis. 

Comparison  of  Course  of  Growth  in  Body  Weight  of 
Original-Entry  and  Reentry  Cows 

The  smooth  curves  in  Fig.  4  describing  the  course  of  growth  in 
the  original-entry  and  reentry  cows  are  plotted  together  for  compar- 


198 


BULLETIN  No.  302 


[January, 


ison  in  Fig.  5.  These  curves,  when  compared,  show  that  on  the  aver- 
age the  reentry  cows  are  distinctly  larger  and  increase  in  weight 
more  rapidly  than  do  the  original-entry  cows.  The  same  relation  is 
indicated  in  the  growth  constants  of  the  equations  of  these  curves. 
The  A  constant,  which  is  the  logarithm  of  the  body  weight  at  ma- 
turity, is  greater  for  the  reentry  cows  than  for  the  original-entry 
cows,  the  values  of  these  constants  being  2.9930  and  2.9793  respec- 
tively. The  greater  value  of  k  for  the  reentry  cows  than  for  the 
original-entry  cows  indicates  a  more  rapid  rate  of  growth  in  the 
former,  the  values  pf  these  constants  being  --  .2993  and  --  .2763 
respectively. 


236 
2.96 

I 

u* 


Reentry  Cows 
Original  'fntry  Co  ivs 


Fig.  5 
ioyto  of  Calculated  Mean  Body  Weighrs 

Equations  of  Curves 
Loa,KW=  Z.9793-. 127344  e~       '    *  Onyrfntry 

Loo,0W  =  2.993O-./34376e    *   93t Reentry 


Fig.  6       Loolo  of  Observed  Mean  Body  Weights 


D — o — vOriginat~  Entry  Cows  without  Reentries 
........ ^Original  Entries  of  Reentry  Cows  only 


Age   in    Years  (Lower  C/ass  Limits) 

FIGS.  5  AND  6. — COMPARISON  OF  BODY-WEIGHT  CURVES 
OF  ORIGINAL-ENTRY  AND  REENTRY  Cows 

The  graphs  in  Fig.  6  represent  the  mean  body  weights  of  the 
original-entry  cows  that  do  not  have  reentry  records  and  the  mean 
body  weights  of  the  original  entries  of  the  reentry  cows  only,  that  is, 
the  mean  body  weights  of  the  reentry  cows  when  they  made  their  first 
or  original-entry  record.  The  mean  body  weights  of  the  original  en- 
tries of  the  reentry  cows  are  not  significantly  different  from  the  mean 
body  weights  of  the  other  original-entry  cows.  In  view  of  this  close 
agreement  between  the  mean  body  weights,  it  is  not  likely  that  the 
reentry  cows  are  selected  for  reentry  on  account  of  their  superior  body 
size.  Hence  it  may  be  assumed  that  the  greater  size  and  more  rapid 
rate  of  growth  found  in  the  reentry  cows  is  due  largely  to  the  more 
favorable  environment  under  which  they  are  kept.  This  conclusion 
is  in  agreement  with  the  experimental  work  of  Eckles  and  Swett  (1918) 
wherein  they  describe  a  difference  in  the  course  of  growth  between 
heavy-fed  Jersey  cows  and  light-fed  Jersey  cows,  similar  to  that  evi- 
denced between  reentry  and  original-entry  Jersey  cows. 


1928}  GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows  199 

Since  increase  in  weight  with  age  may  be  due  to  an  accumulation 
of  inert  substances  within  the  body  cells  rather  than  to  an  increase 
in  the  mass  of  physiologically-active  protoplasm  within  them,  it  is 
desirable  to  supplement  the  body-weight  data  with  growth  measure- 
ments that  bear  directly  upon  the  increase  in  the  mass  of  physiologi- 
cally, active  tissue  with  advancing  age.  The  primary  function  of  a 
dairy  cow  is  the  secretion  of  milk,  that  is,  all  of  her  energy  in  excess 
of  the  requirements  for  maintenance,  gestation  excluded,  is  expended 
in  the  production  of  milk.  Hence  any  change  in  the  activity  of  the 
mammary  gland  with  advancing  age  will  reflect  in  a  general  way  a 
similar  change  in  the  physiological  activity  of  other  organs  of  the  body. 

The  Register-of-Merit  cows,  as  previously  stated,  must  meet  a 
minimum  production  requirement  which  varies  with  their  age.  This 
production  requirement  naturally  eliminates  many  of  the  lower-pro- 
ducing cows  of  the  breed  and  hence,  if  these  Register-of-Merit  pro- 
duction records  are  to  be  used  to  describe  the  course  of  growth  and 
senescence  in  Jersey  cows,  some  correction  must  be  made  for  the 
records  of  the  cows  eliminated  by  the  requirement.  So  far  no  one  has 
attempted  to  estimate  the  number  of  cows  eliminated  by  the  require- 
ment. Most  authors  have  considered  it  of  minor  importance,  assum- 
ing that  the  requirement  eliminated  only  a  small  percentage  of  all 
the  cows  making  the  Register  of  Merit. 

It  will  be  remembered  that  this  production  requirement  is  levied 
upon  the  butterfat  yields  of  the  cows;  therefore  it  was  necessary  to 
study  the  butterfat  yields  rather  than  the  total  milk  yields  of  the  cows. 
This,  however,  causes  no  serious  disturbance  in  the  interpretation,  be- 
cause the  butterfat  content  of  Jersey  milk  contains  in  the  neigh- 
borhood of  60  percent  of  the  total  energy  of  the  yield. 

Tur: \~  CATION  OF  YEARLY  BUTTERFAT  FREQUENCY  DISTRIBUTIONS  DUE  TO 
SELECTIVE  EFFECT  OF  REGISTER-OF-MERIT  REQUIREMENT 

The  frequency  distributions  of  the  yearly  butterfat  yields  at  suc- 
cessive ages  for  the  original-entry  and  reentry  Register-of-Merit  Jer- 
sey cows  are  reported  in  Tables  8  and  9  and  Figs.  7  and  8  respectively. 
The  histograms  in  Fig.  7  showing  the  frequency  distributions  of  the 
yearly  fat  yields  for  the  original-entry  cows  are  severely  truncated. 
The  percentage  of  truncation,  as  will  be  shown  later,  ranges  from  10  to 
39.  The  corresponding  histograms  in  Fig.  8  for  the  reentry  cows, 
however,  are  only  slightly  truncated^  tis  will  likewise  be  shown  later, 
ranging  from  2  to  4  percent.  This  nearly  complete  lack  of  truncation 
of  the  reentry  fat-yield  distributions,  as  compared  to  original-entry 


200 


BULLETIN  No.  302 


[January, 


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1928} 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


201 


Fat  Yield  in  Pounds 


FIG.   7.  —  FREQUENCY   DISTRIBUTIONS   OF   FAT   YIELDS    FOB 
ORIGINAL-ENTRY  JERSEY  Cows 


202 


BULLETIN  No.  302 


[January, 


^/  »«/rf  in  Pounds  Fat  Yteld  i 

FIG.  8.  —  FREXJUENCY  DISTRIBUTIONS  OF  FAT  YIELDS  FOR 
REENTRY  JERSEY  Cows 


fat-yield  distributions,  may  be  attributed  to  the  high  level  of  produc- 
tion of  the  reentry  cows,  that  is,  their  production  is  apparently  beyond 
that  specified  by  the  Register-of-Merit  production  requirement.  Owing 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


203 


YaH  in  Cut.   (liwer  clan  linns') 


FIG.  9. — YEARLY   MILK  YIELDS  OF  REGISTER-OF-MERIT 
JERSEY  Cows  UNDER  Six  YEARS 


/ 

7 

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fli/Mit/d  trr  C*t.  (inter  C/oss  l/m'ts) 

FIG.  10. — YEARLY  MILK  YIELDS  OF  REGISTER-OF-MERIT 
JERSEY  Cows  OVER  Six  YEARS 


to  this  practical  completeness  of  the  yearly  fat-yield  frequency  dis- 
tributions of  the  reentry  cows,  they  were  considered  as  the  type  repre- 
sentative of  yearly  fat-yield  frequency  distributions  for  all  purebred 
Jersey  cows. 

A  further  analysis  of  these  reentry  fat-yield  frequency  distribu- 
tions revealed  the  fact  that  they,  like  the  actual  body-weight  frequency 
distributions,  are  not  symmetrical  but  are  skewed  in  the  positive  direc- 
tion. Here  again  these  fat-yield  distributions  when  transformed  to 
the  logarithmic  scale  become  symmetrical  and  can  be  described  by  the 
log-transformed  equation  of  the  normal  frequency  curve  previously 


204  BULLETIN  No.  302  [January, 

cited.  This  peculiarity  of  these  fat-yield  frequency  distributions  sug- 
gests that  the  factors  affecting  yearly  butterfat  yield  likewise  tend  to 
have  a  constant  percentage  effect  rather  than  an  absolute  effect.  This 
same  peculiarity  is  also  found  in  the  frequency  distributions  of  the 
yearly  milk  yields  for  the  reentry  cows  reported  in  Figs.  9  and  10. 

Before  going  further  into  a  discussion  of  these  reentry  fat-yield 
frequency  distributions,  it  might  be  well  to  give  a  brief  discussion  of 
the  significance  of  the  constants  of  this  log-transformed  frequency 
curve.  Heretofore  it  has  been  assumed  that  the  arithmetic  mean  and 
standard  deviation  were  appropriate  statistics  to  measure  the  varia- 
bility in  the  milk  yields  of  dairy  cows.  The  use  of  the  arithmetic 
mean  and  standard  deviation  presupposes  that  the  frequency  distri- 
bution of  the  data  is  symmetrical.  This,  however,  as  has  been  demon- 
strated, is  not  true  in  the  case  of  milk  and  fat  yield  as  well  as  body 
weight.  Galton  (1879)  pointed  out  that  the  ordinary  law  of  frequency 
of  error  based  on  the  arithmetic  mean  demands  that  deviations  in  excess 
of  the  mean  must  be  balanced  by  deviations  of  equal  magnitude  in 
deficiency.  In  other  words,  the  frequency  distributions  must  be  sym- 
metrical. He  also  pointed  out  that  in  some  cases  where  the  deviations 
in  excess  of  the  mean  are  greater  than  those  in  deficiency,  the  geomet- 
ric mean  and  not  the  arithmetic  mean  best  represents  the  mean  of  the 
data.  McAlister  (1879),  who  at  Galton's  suggestion  gave  a  mathemat- 
ical proof  of  the  applicability  of  the  geometric  mean  to  such  data, 
essentially  assumed  the  existence  of  this  peculiarity  of  the  factors 
affecting  the  data.  When  the  body-weight,  milk-yield,  and  fat-yield 
frequency  distributions  are  transformed  to  the  log  scale,  they  become 
symmetrical,  and  hence  the  arithmetic  mean  and  the  standard  devia- 
tion are  appropriate  statistics  to  apply  on  this  scale.  The  arithmetic 

mean  of  the  log  scale  is  -    — — ,  which  equals  log\/xi-  x2  •  x3 xn, 

which  in  turn  is  the  logarithm  of  the  geometric  mean  on  the  original 
scale.  The  standard  deviation  on  the  log  scale,  when  interpreted  on 
the  original  scale,  approximates  the  logarithm  of  (1  -f  the  coefficient  of 
variation)  and  seems  to  be  the  best  measure  of  the  percentage  varia- 
bility in  data  of  this  type. 


Application  of  Log -Trans  formed  Normal  Frequency  Curve  to 

Yearly  Fat-Yield  Frequency  Distributions  of 

Reentry  Cows 

The  smooth  curves  describing  the  yearly  fat-yield  frequency  dis- 
tributions for  the  reentry  cows  in  Fig.  8  are  fitted  log-transformed 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


205 


frequency    curves,    the    general    equation    of    these    curves    being 


1 


y  = 


.s.r 


\/2i 


_    rlogz-012 


where  x  =  the  fat  yield  and  a  and  s  are  the  mean  and  standard  devia- 
tion on  the  log  scale.  The  means  (a)  and  the  standard  deviations 
(s)  of  these  fitted  curves,  together  with  the  probability  values  (P) 
measuring  their  goodness  of  fit,  are  reported  in  Table  10.  It  will  be 
noted  that  the  probability  values  of  the  goodness  of  fit  of  these  curves, 
with  few  exceptions,  indicate  that  there  is  a  remarkably  close  agree- 
ment between  the  observed  and  calculated  frequencies  in  the  distri- 
butions. In  view  of  this  exceptionally  good  fit  of  the  log-transformed 
normal  frequency  curve  to  the  reentry  fat-yield  frequency  distribu- 
tions, it  was  assumed  that  the  frequency  curve  which  best  describes 
the  yearly  fat-yield  frequency  distributions  characteristic  of  purebred 
Jersey  cows  is  the  log-transformed  normal  curve. 


TABLE  10. — STATISTICS  OF  LOG-TRANSFORMED  NORMAL  CURVE  FITTED  TO  FAT 
YIELDS  OF  REENTRY  JERSEY  Cows 


Age  in  years 

a 

s 

Fre- 
quency 

n* 

X5 

P** 

2.5-3.0 

2.6460  ±  .0098 

.08594  ±  .0069 

35 

3 

10.1639 

.02 

3.0- 

2.6750  ±  .0044 

.10150  ±  .0031 

245 

7 

2.0768 

.95 

3.5- 

2.6915  ±  .0044 

.10090  +  .0031 

238 

7 

7.4892 

.38 

4.0- 

2.7075  ±  .0037 

.09346  ±  .0026 

285 

7 

6.3937 

.50 

4.5- 

2.7220  ±  .0038 

.08783  ±  .0027 

247 

6 

2.3799 

.88 

5.0- 

2.7175  ±  .0036 

.08645  ±  .0026 

260 

6 

10.4279 

.11 

5.5- 

2.7340  ±  .OO44 

.10120  ±  .0031 

242 

8 

8.4483 

.39 

6.0- 

2.7400  ±  .0043 

.08862  ±  .0030 

194 

7 

4.1042 

.77 

6.5- 

2.7315  ±  .0049 

.09531  ±  .0035 

169 

7 

20.1871 

.01 

7.0- 

2.7440  ±  .0050 

.09300  ±  .0035 

158 

7 

5.2092 

.64 

7.5- 

2.7410  ±  .0056 

.09623  ±  .0040 

133 

7 

2.6176 

.91 

8.0- 

2.7590  ±  .0072 

.10690  ±  .0051 

101 

7 

6.0326 

.54 

8.5- 

2.7525  ±  .0071 

.09290  ±  .0051 

78 

6 

20.7688 

.002 

9.0- 

2.7375  ±  .0062 

.09966  ±  .0044 

118 

6 

4.4881 

.61 

10.0- 

2.7440  ±  .0090 

.09300  ±  .0063 

49 

4 

2.8702 

.58 

11.0- 

2.7410  ±  .0118 

.10740  ±  .0083 

38 

3 

1  .  9832 

.58 

13.4*** 

2.7250  ±  .0094 

.08621  +  .0067 

38 

2 

2.2453 

.33 

*Number  of  —  —  terms  corrected  for  the  loss  of  3  degrees  of  freedom,  viz.,  total  frequency,  a 

and  s. 

**A  value  of  P  equal  to  .  10  or  greater  may  be  considered  as  representing  a  close  agreement  between 
the  observed  and  fitted  frequencies.    The  larger  the  value  of  P,  of  course  the  closer  the  agreement. 

***Average  age  of  cows  ranging  from  12.0  to  18.5  years  of  age. 


Correction  for  Truncation  of  Yearly  Fat-Yield  Frequency 
Distributions  of  Original-Entry  Cows 

The  original-entry  yearly  fat-yield  frequency  distributions  in 
Fig.  7,  being  severely  truncated,  do  not  represent  the  yearly  fat-yield 
frequency  distributions  of  all  original-entry  Jersey  cows.  However, 
now  that  a  frequency  curve  has  been  found  that  is  representative  of 
the  true  type  of  frequency  distribution  of  the  yearly  fat  yields  of 


206 


BULLETIN  No.  302 


[January, 


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1928]  GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows  207 

Jersey  cows,  it  is  possible  to  fit  this  curve  to  the  truncated  data  as  far 
as  they  go  and  then  by  extrapolation  derive  a  frequency  curve  which 
may  be  assumed  to  be  representative  of  the  yearly  fat-yield  frequency 
distributions  of  the  population  of  which  the  original-entry  cows  are  a 
truncated  sample.  By  extrapolation  of  this  curve  it  is  also  possible 
to  estimate  the  area  of  the  frequency  distribution  cut  off  by  the  trun- 
cation of  the  data.  Pearson  (1902)  found  the  frequency  distribution 
of  the  speed,  that  is,  the  time  consumed  in  running  one  mile,  of  regis- 
tered American  trotting  horses  was  truncated  at  the  speed  required  by 
the  American  Association  for  registration  of  the  horses.  In  order  to 
estimate  the  frequency  distribution  of  the  speed  for  all  American  trot- 
ting horses,  Pearson  changed  the  normal  frequency  curve  into  the 
form  of  a  parabola  y'  =  a  -f-  bx  -f-  ex2,  where  y'=  log  y,  by  taking  the 
logarithm  of  the  frequencies  instead  of  the  actual  frequencies  them- 
selves. In  this  form  the  normal  frequency  curve  was  fitted  by  the 
method  of  moments  to  the  truncated  data  and  by  extrapolation  a 
frequency  curve  was  derived  which  Pearson  assumed  to  be  representa- 
tive of  the  frequency  curve  of  speed  for  all  American  trotters.  In  a 
similar  manner  the  log-transformed  equation  of  the  normal  frequency 
curve  for  Jersey  cows  was  changed  into  the  form  of  a  parabola 
y'  =  a  -f-  bx'-\-c(x?)2  where  y'  =  log  y  and  x'=  log  x,  and  by  the 
method  of  least  squares  was  fitted  to  the  truncated  original  fat-yield 
frequency  distributions.  The  method  of  fitting  these  curves  is  de- 
scribed in  detail  in  the  Appendix.  The  fitted  curves  in  every  case  were 
extrapolated  and  by  this  procedure  curves  were  derived  intended  to 
be  representative  of  the  untruncated  populations.  The  means  (a)  and 
the  standard  deviations  (s)  of  these  fitted  curves,  the  probability 
values  (P)  measuring  their  goodness  of  fit,  and  the  percentage  of  trun- 
cation of  the  frequency  distributions  estimated  from  the  extrapolation 
of  these  fitted  curves  are  reported  in  Table  11.  The  probability  values 
(P)  of  the  goodness  of  fit  of  these  curves  indicate  that  there  is  a  close 
agreement  between  the  observed  and  fitted  frequencies  in  the  distri- 
butions. The  fit  of  the  smooth  curves  to  the  actual  data  may  be  seen 
in  Fig.  7. 

Truncation  of  Yearly  Milk-Yield  Frequency  Distributions 
of  Original-Entry  Cows 

The  frequency  distributions  of  the  yearly  milk  yields  for  the 
original-entry  and  reentry  Jersey  cows  are  reported  in  Tables  12  and 
13  and  Figs.  9  and  10.  The  frequency  distributions  of  the  yearly  milk 
yields  for  the  reentry  cows,  as  mentioned  before,  are  of  the  same  type 


208 


BULLETIN  No.  302 


[January, 


TABLE  12. — FREQUENCY  DISTRIBUTIONS  OF  365-DAY  MILK  YIELDS  FOR 
ORIGINAL-ENTRY  JERSEY  Cows 


Age  1.5  to  6.0  years 

Age  6.0  to  14.0  years 

Milk  yield 
in  cwt. 

Frequency 
observed 

Percentage 
frequency 
observed 

Percentage 
frequency 
calculated 

Frequency 
observed 

Percentage 
frequency 
observed 

Percentage 
frequency 
calculated 

35-40 

.40 

40- 

56 

'.71 

1.25 

45- 

235 

2.98 

3.12 

50- 

560 

7.09 

5.85 

'.48 

55- 

733 

9.28 

8.79 

'5 

'.28 

1.22 

60- 

962 

12.20 

11.13 

34 

1.91 

2.84 

65- 

972 

12.31 

12.24 

97 

5.46 

5.23 

70- 

989 

12.53 

12.12 

163 

9.17 

7.98 

75- 

794 

10.06 

10.94 

232 

13.06 

10.38 

80- 

718 

9.09 

9.18 

216 

12.16 

11.85 

85- 

523 

6.62 

7.31 

221 

12.44 

12.10 

90- 

388 

4.92 

5.49 

182 

10.24 

11.31 

95- 

278 

3.52 

4.00 

156 

8.77 

9.76 

100- 

233 

2.95 

2.79 

116 

6.53 

7.80 

105- 

148 

1.88 

1.91 

100 

5.62 

6.00 

110- 

109 

1.38 

1.26 

79 

4.45 

4.37 

115- 

78 

.99 

.82 

51 

2.87 

3.05 

120- 

42 

.53 

.53 

34 

1.91 

2.06 

125- 

30 

.38 

.33 

30 

1.68 

1.40 

130- 

19 

.24 

.21 

20 

1.13 

.85 

135- 

9 

.11 

.13 

12 

.68 

.53 

140- 

9 

.11 

.08 

10 

.56 

.32 

145- 

4 

.05 

.05 

9 

.50 

.19 

150- 

1 

.01 

.02 

3 

.17 

.12 

155- 

2 

.03 

.02 

4 

.23 

.07 

160- 

1 

.01 

.01 

1 

.06 

.04 

165- 

.01 

1 

.06 

.02 

170- 

'i 

!6i 

.01 

1 

.06 

.03 

175-180 

1 

.01 

.00 

Total 

7895 

100.00 

100.00 

1777 

100.00 

100.00 

a 

2.86300  ±  .0008 

2.09500  +  .0013 

s 

.09835  ±  .0005 

.08103  ±  .0009 

P 

.02 

.0007 

as  the  butterfat  distributions.  The  smooth  curves  describing  the  milk- 
yield  distributions  for  the  reentry  cows  in  Figs.  9  and  10  are  the  fitted 
log-transformed  normal  curves.  The  probability  values  (P)  measuring 
the  goodness  of  fit  of  these  curves  indicate  that  there  is  a  close  agree- 
ment between  the  observed  and  fitted  frequencies.  The  smooth  curves 
describing  the  milk-yield  distributions  for  the  original-entry  cows  in 
Figs.  9  and  10  are  likewise  the  log-transformed  normal  curves.  The 
probability  values  (P)  measuring  the  goodness  of  fit  of  these  curves, 
however,  indicate  that  there  is  a  very  poor  agreement  between  the 
observed  and  fitted  frequencies.  It  will  be  noted  that  the  original- 
entry  milk-yield  distributions  do  not  have  as  great  a  range  as  the 
reentry  milk-yield  distributions,  the  standard  deviations  (s)  of  the 
reentry  fitted  curves  being  considerably  greater  than  the  standard 
deviations  of  the  original-entry  fitted  curves.  The  lack  of  range  in 
the  original-entry  milk-yield  distributions  can,  for  the  most  part,  be 
attributed  to  the  uniform  truncation  of  these  distributions  to  the  left  of 
their  modes.  The  original-entry  fat-yield  distributions,  as  previously 


1928} 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


209 


TABLE  13. — FREQUENCY  DISTRIBUTIONS  OP  365-DAY  MILK  YIELDS 
FOR  REENTRY  JERSEY  Cows 


Age  2  .  5  to  6.0  years 

Age  6.0  to  14.0  years 

Milk  yield 
in  cwt. 

Frequency 
observed 

Percentage 
frequency 
observed 

Percentage 
frequency 
calculated 

Frequency 
observed 

Percentage 
frequency 
observed 

Percentage 
frequency 
calculated 

50-55 

9 

.58 

.94 

55- 

21 

1.35 

1.50 

!ia 

60- 

51 

3.29 

2.80 

'6 

ise 

.99 

65- 

77 

4.96 

4.46 

21 

1.98 

1.91 

70- 

109 

7.02 

6.21 

33 

3.11 

3.17 

75- 

128 

8.25 

7.76 

67 

6.31 

4.64 

80- 

129 

8.31 

8.89 

73 

6.87 

6.11 

85- 

152 

9.79 

9.40 

76 

7.16 

7.38 

90- 

148 

9.54 

9.32 

103 

9.70 

8.29 

95- 

126 

8.12 

8.82 

74 

6.97 

8.69 

100- 

117 

7.54 

7.95 

90 

8.47 

8.68 

105- 

94 

6.06 

6.84 

72 

6.78 

8.27 

110- 

79 

5.09 

5.76 

91 

8.57 

7.56 

115- 

71 

4.57 

4.69 

70 

6.59 

6.66 

120- 

67 

4.32 

3.71 

55 

5.18 

5.73 

125- 

48 

3.09 

2.86 

55 

5.18 

4.75 

130- 

34 

2.19 

2.20 

45 

4.24 

3.86 

135- 

23 

1.48 

1.65 

20 

1.88 

3.10 

140- 

23 

1.48 

1.21 

23 

2.17 

2.40 

145- 

17 

1.10 

.88 

20 

1.88 

1.87 

150- 

S 

.52 

.63 

18 

1.70 

1.42 

155- 

9 

.58 

.46 

21 

1.98 

1.05 

160- 

4 

.26 

.32 

9 

.85 

.80 

165- 

5 

.32 

.23 

5 

.47 

.58 

170- 

.16 

8 

.75 

.42 

175- 

'2 

.is 

.11 

3 

.28 

.30 

180- 

.08 

2 

.19 

.23 

185- 

'i 

.06 

.16 

1 

.09 

.14 

190- 

.11 

195-200 

'i 

.'09 

.27 

Total 

1552 

100.00 

100.00 

1062 

100.00 

100.00 

a 

2.94750  ±  .0017 

3.02000  ±  .0020 

s 

.09964  ±  .0012 

.09668  ±  .0014 

P 

.69 

.11 

shown,  are  abruptly  truncated  by  the  Register-of-Merit  production  re- 
quirement and  the  milk-yield  distributions  would  be  similarly  truncated 
if  there  existed  a  perfect  correlation  between  milk  yield  and  fat  yield. 
Gowen  (1919)  found  a  correlation  of  +.89  between  the  milk  yields 
and  fat  yields  of  purebred  Holstein  cows  and  surely  a  similar  correla- 
tion exists  for  Jersey  cows.  The  uniform  truncation  of  the  original- 
entry  milk-yield  distributions  decreases  their  range  and  likewise  the 
goodness  of  fit  of  the  log-transformed  normal  curves  applied  to  them. 


COMPARISON  OF  MEANS  (F)  AND  STANDARD  DEVIATIONS  (o-)  ON 

ORIGINAL  SCALE  WITH  MEANS  (a)  AND  STANDARD 

DEVIATIONS  (s)  ON  LOGARITHMIC  SCALE 

Since  the  arithmetic  means  of  the  yearly  fat  yields  of  the  Regis- 
ter-of-Merit Jersey  cows  have  been  used  extensively  to  demonstrate 
the  rise  and  fall  in  the  rate  of  milk  secretion  of  the  cows  with  advanc- 
ing age,  it  seems  best  to  show  the  relation  which  exists  between  these 


210 


BULLETIN  No.  302 


[January, 


means  and  the  corresponding  geometric  mean  fat  yields  (arithmetic 
means  on  the  log  scale).  The  logarithms  of  the  arithmetic  mean  and 
the  logarithms  of  the  geometric  mean  (values  of  a)  yearly  fat  yields 
at  successive  ages  for  both  the  original-entry  and  reentry  cows  are 
graphed  in  Fig.  11.  It  will  be  noted  that  for  the  reentry  cows  the 
arithmetic  mean  fat  yields  lie  slightly  above  and  tend  to  parallel  the 
geometric  mean  fat  yields.  Since  the  reentry  yearly  fat-yield  fre- 
quency distributions,  from  which  these  statistics  were  derived,  are  not 
truncated  much,  it  may  be  assumed  that  on  the  average  the  arithmetic 
mean  fat  yields  will  be  only  slightly  greater  and  tend  to  parallel  the 
geometric  means  of  the  same  data.  The  arithmetic  mean  fat  yields 


Reentry  Cnts 


jfe  IV  years  ftow ere San  lihitj 

FIG.  11. — ARITHMETIC  AND  GEOMETRIC  MEAN  BUTTERFAT 
YIELDS  OF  REGISTER-OF-MERIT  JERSEY  Cows 


of  the  original-entry  cows,  however,  bear  an  altogether  different  rela- 
tion to  the  corresponding  geometric  mean  fat  yields.  The  difference 
between  these  arithmetic  and  geometric  mean  fat  yields  is  greater  than 
that  found  for  reentry  cows  and  besides  markedly  increases  with  the 
age  of  the  cows.  It  will  be  remembered  that  the  percentage  truncation 
of  the  original-entry  fat-yield  frequency  distributions  increases  with 
the  age  of  cows  from  10  to  39  percent.  Hence  this  increasing  differ- 
ence between  the  arithmetic  mean  and  geometric  mean  fat  yields  of 
the  original-entry  cows  reflects  the  percentage  truncation  of  the  related 
fat-yield  frequency  distributions.  It  is  very  evident  that  the  rate  of 
milk  secretion  of  the  original-entry  cows  with  advancing  age  follows 
a  distinctly  different  course  when  described  by  the  arithmetic  means 
of  the  truncated  fat-yield  data  than  when  described  by  the  geometric 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


211 


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212  BULLETIN  No.  302  [January, 

means  derived  from  the  fitted  and  extrapolated  log-transformed  fre- 
quency curves. 

The  standard  deviations  on  the  original  scale  of  the  yearly  fat 
yields  of  both  the  original-entry  and  reentry  cows  (Table  14)  tend  to 
rise  and  fall  with  advancing  age  of  the  cows.  The  coefficients  of  varia- 
bility of  these  fat  yields  (Table  14),  on  the  other  hand,  practically 
remain  constant.  Gowen  (1924)  describes  a  similar  relation  between 
the  standard  deviations  and  the  coefficients  of  variability  of  the  yearly 
fat  yields  of  purebred  Holstein  cows.  The  standard  deviations  of  the 
yearly  fat  yields  on  the  log  scale  derived  from  the  fitted  log-trans- 
formed curves,  for  both  the  original-entry  and  reentry  cows  (Tables 
10  and  11)  also  practically  remain  constant.  Since  the  standard  de- 
viation on  the  log  scale,  as  previously  stated,  approximated  the  log- 
arithm of  (1  -f-  the  coefficient  of  variation),  it  is  to  be  expected  that 
the  trend  in  these  standard  deviations  (s)  with  advancing  age  should 
be  similar  to  the  trend  in  the  corresponding  coefficients  of  variation  on 
the  original  scale. 

Now  that  the  average  yearly  fat  yields  for  all  original-entry  and 
reentry  Register-of-Merit  cows  have  been  determined,  the  former  free 
from  the  effects  of  truncation,  the  next  step  consists  in  the  study  of 
the  course  of  growth  and  senescence  in  Jersey  cows  as  described  by 
the  rise  and  fall  in  their  yearly  fat  yields  with  advancing  age. 

COURSE  OF  GROWTH  AND  SENESCENCE  AS  DESCRIBED  BY  RISE  AND 
FALL  IN  YEARLY  BUTTERFAT  YIELDS  WITH  ADVANCING  AGE 

The  geometric  means,  values  of  a,  of  the  yearly  fat  yields  for  both 
the  original-entry  and  reentry  cows  (Figs.  12  and  13)  tend  to  increase 
but  at  an  ever-decreasing  rate  with  advancing  age  up  to  a  maximum, 
which  is  attained  at  the  age  of  maximum  production  of  the  cows.  Upon 
reaching  the  age  of  maximum  productivity,  the  mean  fat  yields  change 
in  trend  and  tend  to  decrease  at  an  ever-increasing  rate  as  age  in- 
creases. It  will  be  noted  that  up  to  the  age  of  maximum  production 
the  mean  fat  yields  follow  a  course  similar  to  that  followed  by  the 
mean  body  weights,  and  therefore  supplement  the  body  weights  as  a 
measure  of  growth  in  the  cows.  Brody,  Ragsdale,  and  Turner  (1923b) 
found  a  similar  relation  between  the  arithmetic  mean  fat  yields  and 
body  weights  of  purebred  Jersey  cows.  The  mean  fat  yields  not  only 
supplement  the  body  weights  but  also  provide  a  better  measurement 
of  growth  with  respect  to  the  physiologically-active  body  tissue. 

The  mean  body  weights,  after  attaining  their  maximum  at  ap- 
proximately the  same  age  as  the  mean  fat  yields,  remain  more  or  less 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


213 


constant,  and  hence  no  longer  reflect  the  effect  of  age  on  the  body 
tissues  of  the  cows.  The  mean  fat  yields,  however,  after  the  age  of 
maximum  production,  take  a  downward  course  and  steadily  decline 
as  age  advances.  This  steady  decline  in  the  mean  fat  yields  after 


Sf*  in  Years  (lo 

FIG.  12. — GEOMETRIC  MEANS  (a)  AND  STANDARD  DEVI- 
ATIONS (s)  OF  YEARLY  BUTTERFAT  YIELDS  FOR 
ORIGINAL-ENTRY  Cows 


V" 
*j'« 

l" 

15    •»<« 


4.0     fa      t*     7«     ao      ra     M*     •/>     it 
Aje  /»  Ufart  fawer  dost  limts) 


FIG.  13. — GEOMETRIC  MEANS  (a)  AND  STANDARD  DEVI- 
ATIONS (s)  OF  YEARLY  BUTTERFAT  YIELDS 
FOR  REENTRY  Cows 

the  age  of  maximum  production  may  therefore  be  used  as  a  measure 
of  the  influence  of  age  on  the  physiological  activity  of  the  cows  dur- 
ing senility.  Brody  et  al  (1923c)  referred  to  this  decline  in  the  yearly 
fat  yields  during  senility  as  a  measure  of  senescence  in  the  cows; 
in  other  words,  the  process  of  senescence  was  interpreted  as  apply- 


214  BULLETIN  No.  302  [January, 

ing  only  to  the  decline  in  the  physiological  activity  of  the  cows 
after  the  age  of  maturity.  Gowen  (1924)  also  gives  a  similar  inter- 
pretation to  this  decline  in  the  rate  of  milk  secretion  after  the  age  of 
maximum  production.  Such  an  interpretation  of  the  process  of  senes- 
cence would  lead  one  to  believe  that  it  is  initiated  by  the  onset  of 
senility  and  is  represented  by  the  decline  in  the  physiological  activity 
of  the  cells  during  old  age.  Altho  the  evidence  of  senescence  becomes 
very  marked  during  senility,  the  process  as  a  whole  needs  a  broader 
and  more  general  interpretation  than  that  given  by  Brody  and  Gowen. 

Senescence  the  Result  of  Same  Processes  Which  Determine 
Growth  and  Differentiation 

Review  of  Literature. — Minot  (1908)  defined  senescence  as  the  process  of 
growing  old  and  associated  it  with  the  fundamental  processes  of  growth  and  dif- 
ferentiation. He  presented  evidence  based  upon  the  growth  increments  of  rabbits, 
guinea  pigs,  and  chicks  to  show  that  the  rate  of  growth  is  highest  in  the  young 
organism  and  decreases  as  development  proceeds  and  the  rate  of  metabolism 
falls.  He  considers  the  rate  of  growth  as  a  measure  of  the  rate  of  senescence  and 
therefore  concludes  that  the  rate  of  senescence  is  highest  in  youth  and  slowest  in 
advanced  life.  Minot  explains  the  phenomenon  of  senescence  on  the  basis  of  the 
cytoplasmic  changes  taking  place  with  age  and  presents  evidence  to  show  that 
growth  and  differentiation  of  the  cytoplasm  are  the  fundamental  factors  in  senes- 
cence and  death.  He  finds  that  in  the  young  cell  the  amount  of  cytoplasm  in 
relation  to  the  amount  of  nuclear  substance  is  least,  but  that  during  development 
the  cytoplasm  increases  in  proportion  to  the  nuclear  material,  undergoes  differen- 
tiation, and  brings  about  senescence.  Minot,  however,  did  not  explain  how  these 
changes  in  the  cytoplasm  bring  about  senescence.  Child  (1915)  agrees  with  Minot 
in  regarding  the  decrease  in  the  growth  power  of  the  cells  with  advancing  age  as 
evidence  of  senescence,  and  also  associates  it  with  the  cytoplasmic  changes  in  the 
cells  as  age  increases.  Child,  however,  finds  the  cause  of  senescence  in  the  ever- 
increasing  mass  of  inactive  protoplasm  in  the  cells  accompanying  growth  and  dif- 
ferentiation. As  the  mass  of  inactive  protoplasm  increases,  the  mass  of  active  pro- 
toplasm decreases,  and  hence  the  relative  rate  of  metabolism  decreases,  which  in 
turn  brings  about  a  decrease  in  the  reproductive  power  of  the  cells.  Child,  there- 
fore, regards  senescence  as  "primarily  a  decrease  in  the  rate  of  the  dynamic  pro- 
cesses conditioned  by  the  accumulation,  differentiation  and  other  associated 
changes  of  the  material  colloid  substratum."  Consequently  senescence  is  an  in- 
evitable feature  of  growth  and  differentiation  and  is  not  limited  to  the  senile 
stages  in  the  life  cycle. 

In  the  light  of  the  more  general  interpretation  of  senescence,  it 
appears  logical  to  assume  that  the  whole  course  of  milk  secretion  in 
purebred  Jersey  cows  from  youth  to  old  age  is  an  expression  of  the 
senescent  changes  accompanying  the  growth  and  differentiation  of 
their  mammary  glands.  One  of  the  outstanding  features  of  senescence, 


1928}  GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows  215 

according  to  the  above  view,  is  the  continuous  decrease  in  the  repro- 
ductive capacity  (growth  power)  of  the  cells  with  advancing  age. 
Such  a  process  must  necessarily  be  taking  place  in  the  mammary 
glands  if  their  course  of  growth  up  to  the  age  of  maximum  production 
may  be  described  by  the  ever-decreasing  rate  of  increase  in  the  mean 
fat  yields.  Another  outstanding  feature  of  senescence,  and  according 
to  Child  the  cause  of  this  continuous  decrease  in  the  growth  power  of 
the  cells,  is  the  increase  in  the  mass  of  inactive  protoplasm  in  the  cells 
accompanying  growth  and  differentiation.  As  the  mass  of  inactive  pro- 
toplasm in  the  cells  increases,  the  mass  of  active  protoplasm  decreases 
and  likewise  the  relative  rate  of  metabolism  and  functional  activity 
of  the  cells.  In  other  words,  the  relative  functional  activity  of  the 
cells  in  a  gland  constantly  decreases  as  age  increases.  During  the 
earlier  stages  of  growth  in  a  gland  there  is  a  rapid  increase  in  the 
number  of  functional  cells  and  the  total  functioning  capacity  of  the 
gland  increases  regardless  of  the  loss  due  to  the  decrease  in  the  rela- 
tive functional  activity  of  the  component  cells.  However,  a  point  is 
ultimately  reached  where  the  increase  in  the  number  of  functional 
cells  does  not  compensate  for  the  decrease  in  the  relative  functional 
activity  of  the  component  cells  and  the  total  functioning  of  the  gland 
begins  to  decrease.  Such  a  process  would  bring  about  a  change  from 
a  rising  to  a  falling  trend  in  the  total  functioning  of  the  gland  with 
advancing  age.  Considering  the  function  of  the  mammary  gland  from 
this  standpoint,  a  similar  process  must  necessarily  be  taking  place 
within  it,  if  the  rise  and  fall  in  the  mean  fat  yields  may  be  used  as 
a  measure  of  its  functional  activity  with  advancing  age.  Hence  the 
process  of  senescence  is  indicated  just  as  clearly  in  the  ever-decreasing 
rate  of  increase  in  the  mean  fat  yields  up  to  the  age  of  maximum  pro- 
duction as  in  the  ever-increasing  rate  of  decrease  in  the  mean  fat 
yields  beyond  the  age  of  maximum  production.  In  other  words,  the 
process  of  senescence  is  an  inevitable  consequence  of  development 
and  its  evidences  are  ever  present  regardless  of  whether  the  organism 
is  in  the  growing  or  senile  phases  of  the  life  cycle. 

The  course  of  growth  and  senescence  in  these  purebred  Register- 
of-Merit  cows,  as  described  by  the  rise  and  fall  in  their  yearly  fat 
yields  with  advancing  age,  may  also  be  expressed  in  the  form  of  a 
mathematical  equation,  providing  an  equation  can  be  derived  which 
not  only  represents  the  trend  of  the  data  but  which  also  may  be  inter- 
preted upon  the  basis  of  the  biological  phenomena  involved  in  the 
more  general  theory  of  growth  and  senescence. 


216  BULLETIN  No.  302  [January, 

Curves  Describing  Course  of  Growth  and  Senescence 
as  Measured  by  Lactation  in  Dairy  Cows 

Review  of  Literature. — Pearl  (1919)  and  Gowen  (1924)  have  used  the  logar- 
ithmic equation,  y  =  a  +  bx  +  ex2  +  d  log  x  in  which  y  =  milk  yield  and 
x  =  age,  to  represent  the  rate  of  milk  secretion  with  advancing  age  in  all  of  the 
purebred  breeds  of  dairy  cattle.  This  equation  was  fitted  with  a  great  deal  of  ac- 
curacy to  both  the  yearly  milk  yields  and  butterfat  yields  of  Register-of-Merit 
Jersey  cows.  Altho  this  equation  accurately  represents  the  trend  of  the  activity 
of  the  mammary  gland  as  age  increases,  it  is  not  based  upon  any  general  biologi- 
cal law,  and  hence  may  be  considered  as  one  of  many  empirical  equations  which 
change  from  an  increasing  to  a  decreasing  trend  with  increasing  values  of  the  vari- 
ables. Brody  (1923c)  combined  the  yearly  fat  yields,  at  successive  ages,  of  all  the 
purebred  breeds  of  dairy  cattle,  including  the  milking  Shorthorns,  and  found  that 
the  equation  of  two  simultaneous  consecutive  monomolecular  chemical  reactions 
could  be  fitted  to  the  data  with  some  degree  of  accuracy.  This  equation  takes 
the  form  of  M  =  A  (ae~V)  —  be~V)  in  which  fc2  and  k\  are  the  velocity  constants 
of  growth  and  senescence  respectively,  M  =  the  fat  yield  and  t  —  age.  In  order 
to  give  a  biochemical  interpretation  to  this  equation,  Brody  and  his  coworkers 
assume  that  growth  and  senescence  go  on  simultaneously  from  the  beginning  to 
the  end  of  life,  which  assumption  is  not  in  harmony  with  their  earlier  statement. 
Their  interpretation  of  this  chemical  equation  is  very  clearly  stated  in  the  follow- 
ing quotation :  "The  whole  course  of  milk  secretion  with  age  was  therefore  found 
to  follow  approximately  the  course  of  two  simultaneous  consecutive  monomole- 
cular reactions.  This  is  taken  to  mean  that  growth  and  senescence  go  on  simul- 
taneously from  the  beginning  to  the  end  of  life,  and  that  each  follows  an  ex- 
ponential law  with  age;  and  therefore  perhaps  that  the  course  of  the  two  pro- 
cesses are  limited  by  two  consecutive  chemical  reactions."  Altho  there  is  a  sim- 
ilarity between  the  course  of  milk  secretion  with  advancing  age  and  the  course  of 
two  consecutive  monomolecular  chemical  reactions,  it  seems  rather  absurd  to  as- 
sume that  such  a  complicated  physiological  function  as  milk  secretion  is  due  to 
two  simple  chemical  reactions.  Furthermore,  this  equation  separates  growth  (fc2) 
and  senescence  (/d)  into  two  distinct  processes,  a  separation  that  cannot  be  justi- 
fied according  to  the  more  generally  accepted  conception  of  senescence. 

If  it  may  be  assumed  that  the  increasing  trend  in  the  yearly  fat 
yields  up  to  the  age  of  maximum  production,  for  both  the  original- 
entry  and  reentry  cows,  reflects  in  the  main  the  growth  of  their  mam- 
mary glands,  then  the  growth  equation  of  the  type  used  describing  the 
increase  in  body  weight,  logio-M"  =  A  —  be~kt,  where  M  =  fat  yield,  may 
be  used  to  describe  this  trend  in  the  yearly  fat  yields.  Beyond  the 
age  of  maximum  productivity,  however,  the  yearly  fat  yields  of  the 
cows  change  in  trend  and  follow  a  decreasing  course  as  age  increases. 
This  declining  trend  in  the  yearly  fat  yields  after  the  age  of  maxi- 
mum production  may  be  assumed  to  represent  the  effect  of  senility  in 
the  mammary  glands  of  the  cows.  Hence  if  the  above  growth  equa- 
tion is  to  be  used  to  represent  the  whole  course  of  milk  secretion  with 
advancing  age,  a  corrective  term  must  be  added  to  it  in  order  to  ac- 


1928}  GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows  217 

count  for  this  decline  in  the  fat  yields  during  senility.  After  the  addi- 
tion of  a  corrective  term,  this  growth  equation  takes  the  form  of 
logio  M  =  A  —  be~klt  —  dekli  in  which  M  =  the  fat  yield  and  t  =  age 
measured  in  units  of  6  months,  beginning  with  1  year  3  months  as  the 
origin.  The  significance  of  the  other  constants  will  be  brought  out  in 
the  following  discussion.  The  first  part  of  the  above  equation 

logio  M  =  A  —  be~hlt  may  be  interpreted  in  a  similar  manner  as  pre- 
viously described  under  the  section  on  growth  in  body  weight,  and 
broadly  speaking  represents  the  increase  in  fat  yields  due  to  the 
growth  of  the  mammary  gland.  The  function  of  the  mammary  gland, 
however,  depends  not  only  upon  the  number  of  cells  composing  it,  but 
also  upon  the  relative  physiological  activity  of  the  cells.  The  physi- 
ological activity  of  the  cells  depends  upon  the  amount  of  active  proto- 
plasm within  them,  and  since  this  constantly  decreases  with  age  and 
apparently  at  an  ever-increasing  rate,  their  relative  physiological 
activity  likewise  decreases.  Hence  the  corrective  term  deM  that  in- 
creases at  an  ever-increasing  rate  as  age  increases,  must  be  subtracted 
from  logio  M  =  A  —  be~klt  in  order  to  account  for  this  decrease  in  the 
relative  physiological  activity  of  the  cells  in  the  mammary  gland  ac- 
companying growth  and  senility.  This  equation  may  be  derived  as 
follows:  letting  M  be  the  milk  production,  N  the  number  of  secreting 
cells,  and  A  a  measure  of  the  physiological  activity  of  the  cells  in 
producing  milk, 

M  =  NA  or  log  M  =  log  N  +  log  A  (5) 

The  rate  of  change  in  the  milk  production  per  unit  of  tissue  would 
then  be 

dM        dN        dA 

Mdt  ~  Ndt       Adt 

where  t  =  time.  The  percentage  change  in  the  number  of  cells  may 
be  considered  as  a  measure  of  the  growth  power  of  the  cells  (P) ,  that  is, 

m  -  p  <7> 

Ndt 

For  convenience  the  percentage  rate  of  decrease  in  the  physiological 
activity  per  cell  may  be  called  S,  that  is, 

dA 


Adt 
Accordingly,  then 

dM 
Mdt 


=  S  (8) 

=  P  -  S  (9) 


218  BULLETIN  No.  302  [January, 

If  the  growth  power  of  the  cells  (P)  falls  off  at  a  uniform  percentage 
rate,  then 

dP 
Pdt~ 

P  =  Cie-klt  (10) 

If  the  percentage  rate  of  loss  in  physiological  activity  in  milk  secre- 
tion per  cell  (S)  is  increasing  at  a  uniform  percentage  rate,  then 

dS 

Sdt  ~    * 

S  =  C#k*  (11) 


which  after  integration  may  be  put  in  the  form  of 

log  M  =  A  -  be~klt  -  deklt  (12) 

In  this  equation  k^  and  k2  are  both  constants  determining  the  velocity 
of  the  senescence  process.  kt  performs  this  function  by  determining 
the  percentage  rate  of  decrease  in  the  growth  power  of  the  cells  and 
kz  by  determining  the  percentage  rate  of  increase  in  the  percentage 
rate  of  loss  in  the  relative  physiological  activity  of  the  cells.a  This 
equation  differs  from  Brody's  equation  in  that  it  involves  a  growth 
equation  of  the  type  used  to  describe  growth  in  body  weight  and  fur- 
thermore is  based  upon  a  broad  biological  rather  than  a  chemical 
theory  of  development. 

The  above  equation  (12)  representing  the  course  of  growth  and 
senescence  during  development  was  applied  to  the  geometric  mean  fat 
yields  at  successive  ages  for  both  the  original-entry  and  reentry 
Jersey  cows.  The  formulas  of  these  fitted  equations  are  respectively : 

log™  M  =  2.67567  -  .203800e~'2349'  -  .0059618e'1133' 
logio  M  =  2.7733      -  .236561e~'2303'  -  .0045624e -0953' 

in  which  M  =  fat  yields  and  t  =  age  in  units  of  six  months,  beginning 
with  1  year  3  months  as  the  origin.  The  values  calculated  from  these 
fitted  equations  are  reported  in  Tables  15  and  16  respectively.  The 


"The  term  deV  is  approximately  d  +  k-it  when  h*  is  small.  Thus  dk-i  is  the 
approximate  velocity  constant  of  the  percentage  rate  of  decline  in  the  physiologi- 
cal activity  of  the  cells. 


1928] 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


219 


TABLE  15. — MEANS  (a)  AND  STANDARD  DEVIATIONS  (s)  OP  YEARLY  FAT  YIELDS  AT 
SUCCESSIVE  AGES  FOR  ORIGINAL-ENTRY  JERSEY  Cows 


Age  in  years 

Logio  geometric  mean  (a) 

Standard  deviation  on  logio  scale  («) 

Observed* 

Calculated** 

Observed* 

Calculated*** 

1.5-2.0 

2.51050 

2.50784 

.09895 

.09982 

2.0- 

2  .  54222 

2.54077 

.10134 

.100231 

2.5- 

2.56032 

2.56653 

.10405 

.100643 

3.0- 

2.58806 

2.58663 

.09524 

.  101056 

3.5- 

2  .  58795 

2.60218 

.  10866 

.  101469 

4.0- 

2.62293 

2.61410 

.09369 

.  101882 

4.5- 

2.62984 

2.62311 

.09790 

.  102295 

5.0- 

2.62578 

2.62978 

.09964 

.  102708 

5.5- 

2.64362 

2.63452 

.09668 

.103120 

6.0- 

2.63695 

2.63769 

.  10570 

.  103533 

6.5- 

2.62338 

2.63954 

.11602 

.  103946 

7.0- 

2.63441 

2.64027 

.10954 

.  104359 

7.5- 

2.62707 

2.64003 

.11994 

.  104772 

8.0- 

2.64535 

2.63892 

.10467 

.  105184 

8.5- 

2.61294 

2.63701 

.08708 

.  105597 

9.  fl- 

2.62339 

2.63267 

.11307 

.106217 

lC.  0- 

2.63731 

2.62440 

.  10366 

.  107042 

11.0-12.0 

2.61312 

2.61301 

.10627 

.  107868 

13.0**** 

2  .  58522 

2.58920 

.  10875 

.  108694 

*The  observed  values  of  a  and  s  are  the  constants  of  the  log-transformed  frequency  curves  fitted 
to  the  yearly  fat-yield  frequency  distributions  in  Fig.  7. 

**The  calculated  values  of  a  were  derived  from  the  equation  logio  M  =  2.67567  —  .  2038e~-1S4" 
—  .00596 18e-1133'  where  t  =  age  in  units  of  6  months  with  the  origin  at  1  year  3  months  and  logio  M  = 
values  of  a. 

***The  calculated  values  of  s  were  derived  from  the  equation  s  =  .099405  +  .00041282J,  where  t 
=  age  in  units  of  6  months  beginning  with  1  year  3  months  as  the  origin. 

****Average  age  of  cows  ranging  from  12.0  to  18.  5  years  of  age. 


TABLE  16. — MEANS  (a)  AND  STANDARD  DEVIATIONS  (s)  OF  YEARLY  FAT  YIELDS  AT 
SUCCESSIVE  AGES  FOR  REENTRY  JERSEY  Cows 


Age  in  years 

Logio  geometric  mean  (a) 

Standard  deviation  on  logio  scale  (s) 

Observed* 

Calculated** 

Observed* 

Calculated*** 

2.5-3.0 

2.6460 

2.64865 

.08594 

.09386 

3.0- 

2.6750 

2.67224 

.  10150 

.09400 

3.5- 

2.6915 

2.69114 

.10090 

.09414 

4.0- 

2.7075 

2.70580 

.09346 

.09429 

4.5- 

2.7220 

2.71721 

.08783 

.09443 

5.0- 

2.7175 

2.72603 

.  08645 

.09457 

5.5- 

2.7340 

2.73276 

.  10120 

.09472 

6.0- 

2.7400 

2.73780 

.08860 

.09486 

6.5- 

2.7315 

2.74149 

.09531 

.09500 

7.0- 

2.7440 

2.74405 

.09300 

.09515 

7.5- 

2.7410 

2.74569 

.09623 

.09529 

8.0- 

2.7590 

2.74656 

.10690 

.09544 

8.5- 

2.7525 

2.74676 

.09290 

.09558 

9.  fl- 

2.7375 

2.74596 

.09966 

.09579 

lC.  0- 

2.7440 

2.74330 

.09300 

.09608 

11.0-12.0 

2.7410 

2.73895 

.  10740 

.09637 

13.4**** 

2.7250 

2.72571 

.08621 

.09694 

*The  observed  values  of  a  and  s  are  the  constants  of  the  log-transformed  frequency  curves  fitted 
to  the  yearly  fat-yield  frequency  distribution  in  Fig.  8. 

**The  calculated  values  of  a  were  derived  from  the  equation  logio  M=  2.7733  —  .236561e--»»°ai 
—  .0045624e  »»"',  where  t  =  age  in  units  of  6  months,  with  the  origin  at  1  year  3  months  and  logio  M 
=  values  of  a. 

***The  calculated  values  of  «  were  derived  from  the  equation  s  =  .093714  +  .000143418*,  where 
t  =  age  in  units  of  6  months,  beginning  with  2  years  9  months  as  the  origin. 

****Average  age  of  cows  ranging  from  12 . 0  to  18.5  years  of  age. 


smooth  curves  in  Figs.  12  and  13  describing  the  rise  and  fall  in  the 
yearly  fat  yields  of  the  original-entry  and  reentry  cows  are  the  fitted 
growth  and  senescence  curves  represented  by  the  above  equations. 


220 


BULLETIN  No.  302 


[January, 


It  will  be  noted  that  the  trends  of  the  fitted  curves  are  in  fair  agree- 
ment with  the  trends  of  the  observed  mean  fat  yields  with  advancing 
age.  Therefore  it  may  be  assumed  that  the  rise  and  fall  of  the  yearly 
fat  yields  of  the  original-entry  and  reentry  Jersey  cows  is  in  agree- 
ment with  the  biological  theory  of  growth  and  senescence  involved  in 

the  equation  log  M  =  A  —  be~klt  —  deklt  and  hence  is  representative 
of  the  same  processes  in  the  development  of  the  cow. 

Comparison  of  Course  of  Growth  and  Senescence  in  Original-Entry 
and  Reentry  Cows 

The  smooth  curves  in  Figs.  12  and  13  describing  the  course  of 
milk  secretion  (yearly  fat  yields)  with  advancing  age  in  the  original- 
entry  and  reentry  Jersey  cows  are  plotted  together  for  comparison  in 
Fig.  14.  A  comparison  of  these  curves  shows  that  there  is  a  marked 


f   «  //  JO         J 


AjeutYeari    (inner cJau bull 


FIG.  14. — GEOMETRIC  MEAN  FAT  YIELDS  OF  ORIGINAL- 
ENTRY  AND  REENTRY  Cows 


difference  between  the  trend  in  the  yearly  fat  yields  of  the  original- 
entry  cows  (whole  population)  and  the  trend  in  the  yearly  fat  yields 
of  the  reentry  cows  as  age  advances.  The  yearly  fat  yields  of  the 
reentry  cows  besides  being  far  superior  to  the  yearly  fat  yields  of  the 
original-entry  cows,  increase  at  a  greater  rate  during  the  period  of 
growth  and  decrease  at  a  slower  rate  during  the  period  of  senility. 
This  same  relationship  may  be  deduced  from  a  comparison  of  the 
velocity  constants  in  the  equations  of  these  smooth  curves  in  Fig.  14. 
The  velocity  constants  (100/cJ,  determining  the  percentage  rate  of 
decline  in  the  growth  power  of  the  mammary  gland  cells,  are  practi- 
cally the  same  for  both  groups  of  cows,  being  —  23.49  percent  for  the 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows  221 

original-entry  cows  and  —  23.03  percent  for  the  reentry  cows.  On 
the  other  hand,  in  the  last  terms,  deklt ,  which  determine  the  rate  of 
decline  in  the  physiological  activity  of  the  mammary  glands,a  both  d 
and  k2  are  greater  for  the  original-entry  than  for  the  reentry  cows. 
In  other  words,  the  more  rapid  rate  of  increase  as  well  as  the  less 
rapid  rate  of  decrease  in  the  mammary  activity  of  the  reentry  cows 
is  due  almost  entirely  to  the  distinctly  lower  rate  of  decline  in  the 
physiological  activity  of  the  cells  composing  their  mammary  glands. 
Since  the  relative  physiological  activity  of  the  mammary  gland 
cells  decreases  at  a  greater  rate  in  the  original-entry  than  in  the  re- 
entry cows,  it  necessarily  follows  that  the  original-entry  cows  should 
reach  the  stage  of  maximum  production  sooner  in  life  than  the  reentry 
cows.  Such  is  the  case,  for  the  age  of  maximum  production  in  the 
original-entry  cows  is  7  years  4.42  months,  whereas  in  the  reentry 
cows  it  is  8  years  9.22  months.  Hence  it  is  obvious  that  the  original- 
entry  and  reentry  Jersey  cows  are  distinctly  different  in  their  courses 
of  development  as  measured  by  the  physiological  activity  of  their 
mammary  glands  with  advancing  age.  It  will  be  interesting  to  note 
at  this  point  that  Robertson  and  Ray  (1920)  have  found  that  over- 
growth in  mice,  due  to  heavy  feeding,  is  correlated  with  late  maturity 
and  long  life.  The  individuals  showing  overgrowth  are  very  highly 
resistant  to  external  disturbing  factors  and  tend  towards  a  relative 
paucity  of  tissue  (inert  tissue)  accretion  late  in  life.  In  view  of 
these  results  of  Robertson  and  Ray,  the  later  maturity  and  slower 
rate  of  senescence  in  the  reentry  cows,  as  measured  by  the  activity 
of  their  mammary  glands,  may  be  attributed  in  part  to  the  more 
favorable  environment  under  which  the  cows  are  kept. 

Difference  in  Genetic  Constitution  for  Milk  Production  Between 
Original-Entry  and  Reentry  Cows 

It  was  pointed  out  early  in  the  discussion  that  there  is  a  tendency 
on  the  part  of  breeders  to  select  only  the  better-producing  cows  for 
reentry  in  the  Register  of  Merit.  This  selection  if  practiced  to  an 
appreciable  extent  would  bring  about  a  genetic  difference  for  milk 
production  between  the  original-entry  and  reentry  cows,  and  such 
seems  to  be  the  case.  The  present  data  and  likewise  the  data  of 
Graves  and  Fohrman  (1925),  who  also  made  a  separate  study  of  the 
yearly  fat  yields  of  the  original-entry  and  reentry  Register-of-Merit 
Jersey  cows,  illustrates  this  genetic  superiority  of  the  reentry  cows. 
The  arithmetic  mean  fat  yields  at  successive  ages  for  reentry  cows, 

"See  footnote,  page  218. 


222 


BULLETIN  No.  302 


[January, 


and  the  original  entries  of  the  reentry  cows,  as  also  the  original  en- 
tries of  cows  without  reentry  records,  are  shown  in  graphs  I,  II,  and 
III  respectively  in  Fig.  15.  It  will  be  noted  that  up  to  the  age  of 
maturity  the  original-entry  fat  yields  of  the  reentry  cows  (II)  lie 
somewhat  above  and  tend  to  parallel  the  yearly  fat  yields  of  the 
other  original-entry  cows  (III).  Beyond  maturity,  however,  there  is 
very  little  difference  between  the  yearly  fat  yields  of  the  two  groups 
of  cows.  Graves  assumed  that  the  difference  between  the  original- 


Oriynaff/ftry  fens  nittlfat 
Reentry 


\Oryinal ' f/t  tries  ef  /tecn/ry  Cm 


fye i*Ytari  (Jewer  class  l/nirs) 

FIG.  15. — ARITHMETIC  MEAN  FAT  YIELDS  OF  REGISTER- 

OF-MERIT  JERSEY  Cows 
(Data  from  Graves,  U.  S.  D.  A.  Bui.  No.  1352) 

entry  yearly  fat  yields  of  the  reentry  cows  (II)  and  their  subsequent 
reentry  fat  yields  (I)  was  due  to  the  superior  development  of  the 
cows  brought  about  by  their  better  environmental  conditions.  Such 
an  assumption,  however,  is  not  entirely  warranted  as  there  is  still  an 
opportunity  for  further  selection  of  the  cows  entered  for  the  third, 
fourth,  fifth,  etc.,  times.  Just  as  the  cows  to  be  entered  for  the  sec- 
ond time  are  selected  on  their  superior  productive  ability  from  all  the 
original-entry  cows,  so  may  the  cows  entered  for  the  third  time  be 
selected  on  their  superior  productive  ability  from  all  of  the  second- 
entry  cows.  In  other  words  there  may  be  a  continual  selection  of 
the  cows  each  time  they  are  chosen  for  further  entry  in  the  Register 
of  Merit.  Such  a  selection,  when  coupled  with  the  superior  develop- 
ment of  the  cows  resulting  from  their  better  environmental  condi- 
tions, would  naturally  boost  the  reentry  fat-yield  curve  higher  and 
higher  above  the  original-entry  fat-yield  curve  with  advancing  age. 
Hence  there  is  no  doubt  but  that  the  superior  productive  ability  of 
the  reentry  cows  is  due  to  the  influence  of  both  environmental  and 


1928] 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


223 


hereditary  factors,  but  owing  to  complexity  of  conditions  it  is  well 
nigh  impossible  to  determine  the  exact  effect  of  either  environment 
or  heredity. 

INFLUENCE  OF  LEVEL  OF  PRODUCTION  UPON  AGE  CURVE 
OF  MILK  SECRETION 

The  percentiles  of  the  yearly  fat-yield  frequency  distributions  for 
the  original-entry  and  reentry  Jersey  cows  are  shown  in  Figs.  16  and 
17  respectively.  These  percentiles  were  computed  from  the  calculated 
(smoothed)  means  (a)  and  standard  deviations  (s)  reported  in  Tables 
15  and  16  respectively.  In  Figs.  16  and  17  the  50-percentiles  are 


>  GconctrK  ffea. 


jfft  /'«  feats  (icmer  e/ast  t/fiit*) 

FIG.  16. — PERCENTILES  OF  YEARLY  FAT  YIELDS  FOR 
ORIGINAL-ENTRY  JERSEY  Cows 


represented  by  the  geometric  mean  fat  yields,  above  and  below  which 
lies  50  percent  of  the  total  area  of  the  yearly  fat-yield  frequency 
curves.  It  will  be  noted  that  a  given  percentage  of  the  area  of  the 
frequency  curves  above  their  means  takes  in  a  greater  range  in  fat 
yield  than  the  same  percentage  of  the  area  of  the  curve  below  their 
means.  This  difference  in  the  range  of  fat  yield  spanned  by  equal 
percentage  areas  of  the  frequency  curves  above  and  below  their  means 
is  due,  of  course,  to  the  skewness  of  the  yearly  fat-yield  frequency 
distributions,  which  in  turn  has  been  interpreted  as  being  the  result 
of  the  constant  percentage  effects  of  the  factors  determining  the  rate 
of  milk  secretion. 


224 


BULLETIN  No.  302 


[January, 


Another  point  of  interest  which  may  be  deduced  from  these 
yearly  fat-yield  percentiles  is  the  fact  that  at  the  higher  levels  of 
production  there  is  a  somewhat  greater  percentage  increase  in  the 
milk  secretion  up  to  the  age  of  maximum  production  than  at  the 


FIG.  17. — PERCENTILES  OF  YEARLY  FAT  YIELDS  FOR 
REENTRY  JERSEY  Cows 

lower  levels  of  production,  and  a  correspondingly  smaller  decrease 
thereafter.  Another  consequence  is  that  at  the  higher  levels  the  age 
of  maximum  production  comes  somewhat  later  in  life  than  at  the 
lower  levels.  These  result  from  the  slight  increase  in  the  values  of 
s  with  age. 

NATURE  OF  SELECTION  OF  REGISTER-OF-MERIT 
PRODUCTION  REQUIREMENT 

Review  of  Literature. — The  nature  of  the  selection  of  the  Register-of-Merit 
production  requirement  has  been  a  matter  of  much  concern  ever  since  the  estab- 
lishment of  the  Register  of  Merit  by  the  American  Jersey  Cattle  Club.  Almost 
every  investigator  who  has  studied  the  production  records  of  the  Register-of- 
Merit  cows  has  in  some  way  or  other  referred  to  the  selective  effects  of  the  re- 
quirement, but  none  have  actually  estimated  the  percentage  of  cows  eliminated. 
Gowen  (1921)  made  a  study  of  the  nature  of  the  selection  of  the  Register-of- 
Merit  production  requirement  and  concluded  that  the  cows  under  2  years  of  age 
and  over  11.8  years  of  age  were  handicapped  more  by  the  requirement  than  the 
cows  of  the  intervening  ages.  He  also  recognized  that  the  cows  in  the  neighbor- 
hood of  5  years  of  age  were  handicapped  more  than  the  cows  of  other  intervening 
ages.  Gowen,  however,  made  no  estimate  of  the  percentage  of  all  the  cows  elim- 
inated by  the  requirement  at  the  various  ages.  Hooper  (1921)  also  made  a  study 


1928]  GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows  225 

of  the  nature  of  the  selection  of  the  Register-of-Merit  production  requirement 
and  concluded  that  2-year-old  Jersey  cows  were  handicapped  the  least  and  5-year- 
old  cows  the  most  by  the  selective  influence  of  the  requirement.  Here  again  no 
estimate  was  made  concerning  the  percentage  of  all  the  cows  eliminated  at  the 
various  ages. 

The  area  of  the  yearly  fat-yield  frequency  distributions  at 
successive  ages  truncated  by  the  Register-of-Merit  production 
requirement  for  both  the  original-entry  and  reentry  cows  is 
shown  in  Figs.  16  and  17  respectively.  The  percentiles  indi- 
cated by  the  broken  lines  under  the  Register-of-Merit  production- 
requirement  curves  in  Figs.  16  and  17  may  be  assumed  to  represent 
the  percentage  of  the  cows  at  each  age  eliminated  by  the  requirement. 
It  will  be  noted,  for  the  original-entry  cows,  that  the  production- 
requirement  curve  just  includes  the  10-percentile  for  cows  2  years  of 
age  and  then  increases  linearly  with  age,  cutting  the  15-  and  20-per- 
centiles,  up  to  the  23-percentile  for  cows  5  years  of  age.  Above  the 
age  of  5  years  the  production  requirement  remains  constant  at  360 
pounds,  but  decreases  in  its  selective  effect  as  it  nears  the  age  of  max- 
imum production,  where  it  just  touches  the  20-percentile.  Beyond 
the  age  of  maximum  production  the  requirement  again  begins  to 
increase  in  its  selective  effect  and  continues  to  increase  thruout  the 
remaining  life  of  the  cows,  cutting  the  39-percentile  at  the  age  of 
13  years.  Hence  it  may  be  assumed  that  the  percentage  of  all  the 
original-entry  cows  at  each  age  eliminated  by  the  requirement  in- 
creases from  10  percent  of  the  2-year-old  cows  to  23  percent  of  the 
5-year-old  cows  and  then  decreases  to  20  percent  of  the  7.5-year-old 
cows,  following  which  it  continually  increases,  eliminating  39  percent 
of  the  13-year-old  cows.  The  production-requirement  curve  in  Fig.  17 
follows  a  similar  trend  in  its  selective  influence  as  age  advances,  but 
eliminates  only  a  very  small  percentage  of  the  reentry  cows.  Less 
than  2  percent  of  the  2-year-old  reentry  cows,  4  percent  of  the  5- 
year-old  cows,  approximately  2  percent  of  the  8.5-year-old  cows  and 
only  4  percent  of  the  13-year-old  cows  are  eliminated  by  the  require- 
ment. Therefore  it  is  obvious  that  the  high  level  of  production  of 
the  reentry  cows  almost  entirely  excludes  them  from  the  selective 
influence  of  the  Register-of-Merit  requirement. 


226  BULLETIN  No.  302  [January, 

SUMMARY 

In  this  study  the  Register-of-Merit  records  of  9,694  original-entry 
and  2,628  reentry  cows  were  analyzed  separately  by  means  of  bio- 
metrical  methods  in  an  effort  to  determine  the  course  of  growth  and 
senescence  in  Jersey  cows. 

Course  of  Growth  in  Body  Weight. — The  increase  in  body  weight 
of  the  cows  with  advancing  age  may  be  expressed  by  the  growth 
equation  \ogwW-—  A  —  be~kt  in  which  W  is  the  weight  at  any  age  t,  and 
A  is  the  logarithm  of  the  body  weight  at  maturity.  100/c  is  the  con- 
stant percentage  rate  of  decrease  in  the  growth  power  per  unit  weight, 
e  is  the  base  of  the  natural  logarithms,  and  b  is  a  constant  locating 
the  curve  in  point  of  time.  The  formulas  of  the  equations  repre- 
senting the  growth  data  for  the  original-entry  and  reentry  cows  are 
respectively : 

logio  W  =  2.9793  -  .12736--2763' 
logio  W  =  2.9930  -  .13446-2993' 

A  comparison  of  the  constants  in  these  equations  shows  that  there  is 
a  distinct  difference  between  the  course  of  growth  in  body  weight  in 
the  original-entry  and  reentry  cows.  The  reentry  cows  attain  a 
greater  weight  at  maturity  and  increase  in  weight  more  rapidly  than 
do  the  original-entry  cows.  Both  groups  reach  their  maximum  weight 
at  approximately  8  years  of  age.  It  was  found  that  there  is  no  genetic 
difference  between  the  original-entry  and  reentry  cows  for  body  size; 
hence  it  may  be  assumed  that  the  greater  size  and  the  more  rapid 
rate  of  growth  of  the  reentry  cows  is  due  largely  to  the  more  favorable 
environment  under  which  they  are  kept. 

Course  of  Growth  and  Senescence  as  Described  by  Rise  and  Fall 
in  Yearly  Butterfat  Yields  with  Advancing  Age. — It  was  necessary 
first  to  correct  for  the  truncation  of  the  yearly  butterfat  frequency 
distributions  of  the  cows,  due  to  the  selective  effect  of  the  production 
requirement  of  the  Register  of  Merit.  The  frequency  distributions 
of  the  reentry  cows  at  successive  ages  are  only  slightly  truncated  at 
the  lower  levels,  whereas  the  distributions  of  the  original-entry  cows 
are  severely  truncated.  It  was  found  that  the  frequency  curve  best 
adapted  to  these  yearly  fat-yield  frequency  distributions  of  both  the 
original-entry  and  reentry  cows  is  the  log-transformed  equation  of  the 
normal  curve 

1  [logo;  — a]  2 
=                   ~    L 


1928]  GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows  227 

in  which  a  and  s  are  the  mean  and  standard  deviation  respectively  on 
the  log  scale.  Owing  to  the  severe  truncation  of  the  original-entry 
distributions,  it  was  necessary  to  fit  them  in  a  peculiar  manner  in 
order  to  determine  the  curves  of  the  whole  populations  of  which  the 
original-entry  cows  are  a  truncated  sample.  The  percentage  of  the 
cows  eliminated  by  the  production  requirement  was  estimated  from 
the  fitted  frequency  curves.  Only  2  percent  to  4  percent  of  the  re- 
entry cows  are  eliminated,  whereas  10  percent  to  39  percent  of  the 
original-entry  cows  are  eliminated. 

The  true  means  of  the  yearly  fat  yields  at  successive  ages  for 
both  the  original-entry  and  reentry  cows  were  determined  by  the  fitted 
log-transformed  frequency  curves.  These  means  increase  with  ad- 
vancing age  up  to  a  maximum  (age  of  maximum  production)  but  at 
an  ever-decreasing  rate,  and  then  decrease  at  an  ever-increasing  rate. 
This  rise  and  fall  in  the  yearly  fat  yields  of  the  cows  may  be  ex- 
pressed in  part  by  an  equation  of  the  same  type  as  the  growth  equa- 
tion representing  the  increase  in  body  weight  with  age.  However,  a  cor- 
rective factor  must  be  added  to  this  equation  in  order  to  take  into  ac- 
count the  decrease  in  the  fat  yields  after  the  age  of  maximum  produc- 
tion. The  corrected  equation  takes  the  form  of  logic  M  =  A  —  be~klt—deklt 
in  which  M  =  fat  yield  at  any  age  t.  The  first  part  of  this  equation, 
logio  M  =  A  —  be~klt  broadly  speaking,  may  be  interpreted  as  repre- 
senting the  increase  in  the  fat  yield  with  advancing  age  due  to  the 
growth  of  the  mammary  gland,  100/c1  being  the  constant  percentage 
rate  of  decrease  in  the  growth  power  per  unit  volume  of  the  gland. 
The  total  function  of  the  mammary  gland,  however,  depends  not  only 
upon  the  number  of  cells  composing  it,  but  also  upon  the  relative 
physiological  activity  of  the  cells.  The  physiological  activity  of  the 
cells  depends  upon  the  amount  of  active  protoplasm  within  them,  and 
since  this  constantly  decreases  with  advancing  age  and  apparently  at 
an  ever-increasing  rate,  their  relative  physiological  activity  likewise 
decreases.  Hence  the  corrective  term  dektt  may  be  said  to  represent 
the  decline  in  the  relative  physiological  activity  of  the  cells  in  the 
mammary  gland  accompanying  growth  and  senility. 

The  theory  of  senescence  involved  in  the  above  interpretation 
may  be  said  to  be  in  accordance  with  the  general  theory  of  senescence 
advanced  by  Child  (1915).  Consequently  the  process  of  senescence 
is  indicated  just  as  clearly  in  the  ever-decreasing  rate  of  increase  in 
the  mean  fat  yields  up  to  the  age  of  maximum  production  as  in  the 
ever-increasing  rate  of  decrease  in  the  mean  fat  yields  beyond  the 
age  of  maximum  production. 


228  BULLETIN  No.  302  [January, 

The  formulas  of  the  equations  representing  the  mean  fat  yields 
with  advancing  age  for  the  original-entry  and  reentry  cows  are  respec- 
tively : 

logic  M  =  2.6757  --  .2038e -2349<  -  .00596e1133' 
logio  M  =  2.7733  -  .2366e~'2303'  -  .00456e'0953< 

These  equations  when  graphed  show  that  there  is  a  distinct  dif- 
ference between  the  rise  and  fall  in  the  yearly  fat  yields  of  the  orig- 
inal-entry and  the  reentry  cows.  The  fat  yields  of  the  reentry  cows 
are  far  superior  to  the  fat  yields  of  the  original-entry  cows  and  in- 
crease at  a  greater  rate  with  advancing  age.  After  the  age  of  maxi- 
mum production  (during  senility)  the  fat  yields  of  the  reentry  cows 
do  not  decline  so  rapidly  as  do  the  fat  yields  of  the  original-entry 
cows.  The  age  of  maximum  production  in  the  reentry  cows  is  8  years 
9.22  months  and  in  the  original-entry  cows  7  years  4.42  months. 

It  was  found  that  the  genetic  difference  for  milk  production  be- 
tween the  original-entry  and  reentry  cows,  altho  significant,  was  not 
great  enough  to  account  entirely  for  the  superior  productive  ability 
of  the  latter.  Hence  it  may  be  assumed  that  both  heredity  and  en- 
vironment play  an  important  part  in  bringing  about  the  distinctly 
superior  rate  of  milk  secretion  in  the  reentry  cows. 


1928}  GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows  229 

LITERATURE  CITED 

BRODY,  SAMUEL 

1926  Time  relations  of  growth.  I.  Genetic  growth  constants  of  animals.  Jour. 

Gen.  Physiol.  8,  233. 
BRODY,  SAMUEL,  AND  RAGSDALE,  ARTHUR  C. 

1921  The  rate  of  growth  in  the  dairy  cow.  Jour.  Gen.  Physiol.  3,  623. 

1922  The  equivalence  of  age  in  animals.  Jour.  Gen.  Physiol.  5,  205. 

1924  Rate  of  growth  of  the  dairy  cow.  V.  Extrauterine  growth  in  linear  di- 

mensions. Jour.  Gen.  Physiol.  6,  329. 
BRODY,  SAMUEL,  RAGSDALE,  ARTHUR  C.,  AND  TURNER,  CHARLES  W. 

1923a  Rate  of  growth  of  the  dairy  cow.   II.  Growth  in  weight  after  the  age 

of  two  years.  Jour.  Gen.  Physiol.   5,  445. 
1923b  Relation  between  growth  in  weight  and  increase  of  milk  secretion  with 

age.  Jour.  Gen.  Physiol.  6,  21. 

1923c  Growth  and  senescence  as  measured  by  the  rise  and  fall  of  milk  se- 
cretion with  age.  Jour.  Gen.  Physiol.  6,  31. 
CHILD,  CHARLES  MANNING 

1915  Senescence  and  rejuvenescence.  University  of  Chicago  Press.  Chicago. 
DONALDSON,  HENRY  HERBERT 

1915  The  rat.    Wistar  Inst.    Mem.  6.   1915. 

ECKLES,  C.  H.,  AND  SwETT,  W.  W. 

1918  Some  factors  influencing  the  growth  of  dairy  heifers.    Mo.  Agr.  Exp. 

Sta.  Res.  Bui.  31. 
ECKLES,  C.  H. 

1920  The  normal  growth  of  dairy  heifers.   Mo.  Agr.  Exp.  Sta.  Res.  Bui.  36. 
FISHER,  RONALD  AYLMEB 

1925  Statistical  methods  for  research  workers.  Oliver  and  Boyd.  Edinburgh, 

London. 
GALTON,  FRANCIS 

1879  The  geometric  mean  in  vital  and  social  statistics.   Roy.  Soc.  (London) 

Proc/29,  365. 
GOWEN,  JOHN  W. 

1919a  Report  of  progress  on  animal  husbandry  investigations  in  1919.   Ann. 

Rpt.  Maine  Agr.  Exp.  Sta.   1919. 

1919b  Variations  and  mode  of  secretion  of  milk  solids.   Jour.  Agr.  Res.  16, 
79. 

1920  Studies  in  milk  secretion.  V.  On  the  variations  and  correlations  of  milk 

secretion  with  age.  Genetics  5,  111. 

1921  Mean  butterfat  yield  of  the  different  breeds  and  the  advanced  registry 

requirements.  Ann.  Rpt.  Maine  Agr.  Exp.  Sta.  1920. 

1924  Milk  secretion.  Williams  &  Wilkins  Co.  Baltimore,  Md. 

1925  Studies  on  conformation  in  relation  to  milk-producing  capacity  in  dairy 

cows.  Jour.  Agr.  Res.  30,  865. 
GRAVES,  R.  R.,  AND  FOHRMAN,  M.  H. 

1925  Effect  of  age  and  development  on  butterfat  production  of  register-of- 

merit  cattle.  U.  S.  Dept.  Agr.  Bui.  1352. 
HOOPER,  J.  J. 

1921  Studies  of  dairy  cattle.  Ky.  Agr.  Exp.  Sta.  Res.  Bui.  234. 

KlLDEE,  H.  H.,  AND   McCANDLISH,  A.  C. 

1916  Influence  of  environment  and  breeding  in  increasing  dairy  production. 

Iowa  Agr.  Exp.  Sta.  Bui.  165. 
LOEB,  JACQUES 

1906  The  dynamics  of  living  matter.  Columbia  University  Press.  New  York. 


230  BULLETIN  No.  302 

McAiJSTER,  DONALD 

1879  The  law  of  the  geometric  mean.  Roy.  Soc.  (London)  Proc.  29,  367. 
McCANDLiSH,  ANDREW  C. 

1920  Environment  and  breeding  as  factors  influencing  milk  production.  Jour. 

Heredity  11,  204. 
MINOT,  CHARLES  S. 

1891  Senescence  and  rejuvenescence.  Jour.  Physiol.  12,  97. 

1908  The  problem  of  age,  growth  and  death.  Putnam's  Sons,  New  York. 

OSTWALD,  WlLHELM 

1908  Vortrage  und  Aufsatze  iiber  Entwicklungsmechanik  der  Organismen. 

Leipzig. 
1908  Uber  die  zeitlichen  Eigenschaften  der  Entwicklungsvorgange.  Vortrage 

und  Aufsatze  iiber  Entwicklungsmech.,  herausgeg  von  Wilh.  Roux, 

Heft  5. 
PEARL,  RAYMOND,  GOWEN,  JOHN  W.,  AND  MINER,  JOHN  RICE 

1919  Studies  in  milk  secretion.  VII.   Transmitting  qualities  of  Jersey  sires 

for  milk  yield,  butterfat  percentage,  and  butterfat.    Ann.  Rpt. 
Maine  Agr.  Exp.  Sta. 
PEARSON,  KARL 

1914  Tables  for  statisticians  and  biometricians.   London. 

1900  On  the  criterion  that  a  given  system  of  deviations,  etc.  Phil.  Mag.  and 

Jour.  Sci.  50,  157. 

1902  On  the  systematic  fitting  of  frequency  curves.  Biometrika  2,  1. 
READ,  J.  MARION 

1912  Intrauterine  growth  cycles  of  the  guinea  pig.   Arch.  Entwickl.  Mech. 

Organ.  35,  708. 
ROBERTSON,  T.  BRAILSFORD 

1916  The  normal  growth  of  the  white  mouse.  Jour.  Biol.  Chem.  24,  363. 

1923  The  chemical  basis  of  growth  and  senescence.  Lippincott.  Philadelphia 

and  London. 
ROBERTSON,  T.  BRAILSFORD,  AND  RAY,  L.  A. 

1920  Experimental  studies  of  growth.  XV  and  XVI.  Jour.  Biol.  Chem.  42 

and  44. 
TURNER,  C.  W.,  RAGSDALE,  A.  C.,  AND  BRODY,  SAMUEL 

1924  The  relation  between  age,  weight  and  fat  production  in  dairy  cows. 

Mo.  Agr.  Exp.  Sta.  Bui.  221. 
VAN  DE  SANDE-BAKHUYZEN,  H.  L.,  AND  ALSBERG,  CARL  L. 

1927  The  growth  curve  in  annual  plants.  Physiol.  Rev.  7,  151. 
WRIGHT,  SEWALL 

1926  A  frequency  curve  adapted  to  variation  in  percentage  occurrence.  Jour. 

Amer.  Statis.  Assoc.  21,  162. 
1926  Reviews.  Jour.  Amer.  Statis.  Assoc.  21,  493. 


APPENDIX 

Fitting  Log-Transformed  Normal  Frequency  Curve  by  Method  of  Least  Squares 

to  Truncated  Yearly  Butterfat  Frequency  Distributions  of  Original-Entry  Regis- 

ter-of-Merit  Jersey  Cows 

(/.  —  /)* 
In  fitting  frequency  curves  Pearson  (1900)  has  shown  that  x1  =    —  7  —  —  ,  where 

/.  =  observed  frequency  and  fc  =  calculated  frequency,  should  be  minimum.  Thus 
an  ordinary  least-square  fit,  (/.  —  /e)2  =  minimum,  gives  too  much  weight  to 
the  high  values  of  /  at  the  expense  of  the  low  values.  The  proper  weighting  may  be 

secured  by  multiplying  the  squared  residuals  by  j  •  For  example,  the  following  dif- 
ferences contribute  equally  to  x2: 

/.  /.  A/  (A/)«  7.(A/)> 

1.10  1  .10  .01  .01 

10.31  10  .31  .10  .01 

101.00  100  1.00  1.00  .01 

In  actual  calculation,  however,  j  must  be  used  as  an  approximation  to  j  •  This, 
of  course,  introduces  an  error,  but  one  of  no  practical  importance. 

In  fitting  the  log  of  frequency  curves,  a  residual  A/  in  the  primary  curve  is 
represented  by  -4-  in  the  log  curve  (since  d  log/  =  -~  J  and  the  squared  residual 

by  ,,  •  •  Therefore  in  fitting  the  log  frequencies  by  least  squares,  each  squared 
residual  should  be  weighted  by  /  in  order  to  make  —  4  —  minimum,  since  ~  •  f  = 
For  example, 

/.  /.  log/0  log/,  Alog/  (Alog/)>  /t(Alog/)« 

1.10  1  .041                 0             .041  .0016                    .0018 

10.31  10  1.013                  1              .013  .00016                  .0016 

101.00  100  2.004                  2              .004  .000016                 .0016 

Here  again  ft  instead  of  ft  must  be  used  in  weighting  in  the  actual  calculation. 

The  equation  of  the  log-transformed  normal  curve  fitted  to  the  truncated 
yearly  fat-yield  frequency  distributions  of  the  original-entry  cows  is 


N' 


flog  x-  a\  2 

—  7—  J 


in  which  N'  =  the  total  frequency  under  the  curve,  including  the  unknown  por- 
tion below  the  Register-of-Merit  production  requirement;  a  and  s  are  the  mean 
and  the  standard  deviation  on  the  log  scale.  It  is  convenient  in  fitting  to  trans- 
form to  logic  z  instead  of  logex  and  to  measure  x  in  100-pound  units.  As  the  class 
ranges  are  in  50-pound  units  (except  for  the  first  class)  the  observed  frequencies 

231 


232  BULLETIN  No.  302  [January, 


give  an  approximation  to  -\y,  ~?QQ~  V,  in  general.  Letting  y  =  fa  =  |  for  complete 
classes 

_  t  pogio  x  —  al  2 
N'  logic  6  JL  g  J 

2/  =  "         K 

This  equation  cannot  be  fitted  by  direct  methods  because  of  the  truncation  of  the 
data.  It  can  be  fitted,  however,  by  taking  the  logarithms  of  the  frequencies, 
which  throws  it  into  the  form  of  a  parabola,  a  convenient  form  for  fitting  by 
least  squares. 

Letting  y'  =  logio  yo  and  x'  =  logio  x 
This  is  of  the  general  form  y'  =  A  +  Bx'-\-  C(x'Y.  Where 


_  a  logio  e  _ 
_  _  _  logio  e 

The  constants  A,  B,  and  C  were  determined  by  the  method  of  least  squares 
as  follows: 

The  general  least-square  normal  equations  of  the  parabola  y'  =  A  +  Ex    + 
C  (x')2,  using  the  weight  fo,  are 

ABC 

fa  +   fa*'  +   /o(*')2     =    ./> 

„(*')    +  /„(*'>*  +  /0(*')3  =  f,x'y 


In  these  formulae  y'  =  log  0/o  except  in  the  first  class  of  each  distribution,  which  is 
of  varying  range.  The  effect  of  the  truncation  is  illustrated  in  Fig.  18.  Taking, 
for  example,  cows  3.5  to  4.0  years  of  age,  the  first  recorded  butterfat  class  is  that 
for  300  to  350  pounds.  This  class  is  truncated  by  the  requirement  to  varying  ex- 
tents indicated  by  the  shading.  An  average  of  the  truncation  is  at  314.4  pounds, 
leaving  a  class  range  of  35.6  pounds  instead  of  the  usual  50  pounds,  and  a  class 
mid-point  of  3322  pounds.  The  observed  frequency  of  104  must  be  rated  up  by  the 

ratio  — —  (giving  146.1)  to  obtain  the  magnitude  of  the  ordinate  on  a  scale  com- 
35.6 

parable  to  those  for  the  complete  classes.   In  this  case  then  y'  —  logio  ( )/<>• 

\range/ 

The  whole  procedure  for  fitting  this  age  class  is  given  in  Table  17. 

The  method  of  determining  the  theoretical  frequencies   (/)   is  reported  in 
Table  18  and  is  the  same  as  that  described  by  Wright  (1926).   N"  in  Table  18 


GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


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GROWTH  AND  SENESCENCE  IN  PUREBRED  JERSEY  Cows 


235 


FIG.  18. — REGISTER-OF-MERIT  PRODUCTION  REQUIREMENT 
CURVE 

was  calculated  from  the  total  frequency  of  the  truncated  data,  2/0  =  636.  As  79.8 
percent  of  the  area  of  the  theoretical  curve  is  above  the  point  of  truncation 
(314.4  pounds)  and  636  cows  are  recorded  above  this  point,  the  percentage  fre- 

G"yc 

quencies  must  be  multiplied  by  =  7.974  to  obtain  the  theoretical  frequen- 

•      /  y.o 

cies  which  will  give  minimum  x2-  This  gives  a  total  theoretical  frequency,  N"  = 
797.4,  slightly  different  from  the  figure  N'  =  800.8,  obtained  from  the  solution  of 
the  normal  equations.  The  latter  is  used  only  as  a  rough  check  to  N".  In  calcu- 
lating the  probability  from  x2,  it  must  be  noted  that  3  degrees  of  freedom  are  lost 
in  the  calculation  of  N'  a,  and  s  from  the  data  (see  Fisher  1925).  The  9  contri- 
butions to  x2  thus  yield  6  degrees  of  freedom  and  in  Elderton's  table  are  entered 
under  ri  =  7  (nr  being  one  greater  than  the  number  of  degrees  of  freedom) . 


UNIVERSITY  OF  ILLINOIS-URBANA 


